prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
arthurpaulino wants to merge 1 commit into
base:master
Choose a base branch
from
Open

prove weak-head reduction weakening #39

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
60 changes: 59 additions & 1 deletion Lean4Lean/Experimental/SExpr.lean
View file
Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
| .true => []
| .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
(r : p.RHS) :
(r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
induction r with
| fixed c h =>
simp only [Pattern.RHS.applyS]
rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
| var => rfl
| app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
(H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
∀ path, m2' path = (m2 path).lift' ρ := by
induction H with
| const => exact ⟨nofun, .const, nofun⟩
| @var _ fn _ _ arg _ ih =>
obtain ⟨g, hg, ih⟩ := ih
rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
fun | none => rfl | some path => ih path⟩
| app _ _ ihf iha =>
obtain ⟨gf, hgf, ihf⟩ := ihf
obtain ⟨ga, hga, iha⟩ := iha
exact ⟨Sum.elim gf ga, .app hgf hga,
fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
(r : p.Check) :
(r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
r.defeqsS m1 fun path => (m2 path).lift' ρ := by
induction r with
| true => rfl
| defeq a b rest ih =>
simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
| .app h1 => .app (h1.weak' W)
| .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
| .extra h1 h2 h3 h4 => sorry
| @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
subst m2'
let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
rw [Pattern.RHS.lift'_applyS]
refine .extra h1 hm (dfs := dfs') ?_ ?_
· rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
unfold dfs'
rw [List.map_map]
simp [liftPair, Function.comp_def]
· intro a b A hab
obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
obtain ⟨A', a', b'⟩ := x
have hw := (h4 a' b' A' hx).weak' W
have hA := congrArg Prod.fst hxeq
have hp := congrArg Prod.snd hxeq
have ha := congrArg Prod.fst hp
have hb := congrArg Prod.snd hp
dsimp [liftPair] at hA ha hb
rw [← hA, ← ha, ← hb]
exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down
, 'i'); if (__m === '*' || __re.test(location.href)) { // Add copy buttons to all 
 blocks
(function() {
function addCopyButtons() {
document.querySelectorAll('pre code').forEach(function(codeBlock) {
if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;
codeBlock.parentElement.setAttribute('data-copy-added', 'true');
var btn = document.createElement('button');
btn.textContent = 'Copy';
btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';
btn.onmouseover = function() { this.style.opacity = '1'; };
btn.onmouseout = function() { this.style.opacity = '0.7'; };
btn.onclick = function() {
navigator.clipboard.writeText(codeBlock.textContent).then(function() {
btn.textContent = 'Copied!';
setTimeout(function() { btn.textContent = 'Copy'; }, 1500);
});
};
codeBlock.parentElement.style.position = 'relative';
codeBlock.parentElement.appendChild(btn);
});
}
addCopyButtons();
// Re-run on dynamic content
var observer = new MutationObserver(addCopyButtons);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Force GitHub README to respect dark mode
(function() {
var style = document.createElement('style');
style.textContent = '
.markdown-body {
color-scheme: dark light;
}
.markdown-body pre { background: #161b22 !important; }
.markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }
.markdown-body table th, .markdown-body table td { border-color: #30363d !important; }
.markdown-body img { background: #0d1117; }
.markdown-body blockquote { border-left-color: #8b949e; }
.markdown-body hr { border-color: #30363d; }
';
document.head.appendChild(style);
})();
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Highlight search terms from Google/DuckDuckGo/Bing referrer
(function() {
var ref = document.referrer;
var terms = [];
if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {
var url = new URL(ref);
var q = url.searchParams.get('q') || url.searchParams.get('p');
if (q) {
terms = q.split(/\s+/).filter(function(t) { return t.length > 2; });
}
}
if (terms.length === 0) return;
var style = document.createElement('style');
style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';
document.head.appendChild(style);
function highlight(node) {
if (node.nodeType === 3) { // text node
var text = node.textContent;
var found = false;
terms.forEach(function(term) {
var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\]\\]/g, '\\') + ')', 'gi');
if (regex.test(text)) {
found = true;
var frag = document.createDocumentFragment();
var parts = text.split(regex);
parts.forEach(function(part, i) {
if (i % 2 === 0) {
frag.appendChild(document.createTextNode(part));
} else {
var span = document.createElement('span');
span.className = 'userscript-highlight';
span.textContent = part;
frag.appendChild(span);
}
});
node.parentNode.replaceChild(frag, node);
}
});
} else if (node.nodeType === 1 && node.childNodes) { // element
var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];
if (!skipTags.includes(node.tagName)) {
Array.from(node.childNodes).forEach(highlight);
}
}
}
highlight(document.body);
// Re-highlight on dynamic content
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1 || node.nodeType === 3) highlight(node);
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Strip utm_, fbclid, gclid, etc. from all links on page
(function() {
var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
u.searchParams.delete(p);
changed = true;
}
});
return changed ? u.toString() : url;
} catch (e) {
return url;
}
}
function cleanLinks() {
document.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
cleanLinks();
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1) {
if (node.tagName === 'A') cleanLinks();
node.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Auto-enable theater mode on YouTube
(function() {
function tryTheater() {
var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]');
if (btn && !btn.classList.contains('activated')) {
btn.click();
}
}
// Try immediately
tryTheater();
// Try after navigation (SPA)
var lastUrl = location.href;
setInterval(function() {
if (location.href !== lastUrl) {
lastUrl = location.href;
setTimeout(tryTheater, 500);
}
}, 1000);
// Also try on player load
var observer = new MutationObserver(tryTheater);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Remove or un-stick sticky/fixed headers that block content
(function() {
function unstick() {
document.querySelectorAll('header, nav, [role="banner"], .header, .navbar, .sticky, .fixed-top, [style*="position: fixed"], [style*="position:sticky"]').forEach(function(el) {
if (el.style.position === 'fixed' || el.style.position === 'sticky' || getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {
el.style.position = 'static';
el.style.top = 'auto';
el.style.zIndex = 'auto';
}
});
}
unstick();
var observer = new MutationObserver(unstick);
observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });
})();
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Universal Dark Mode - works on any site
(function() {
var enabled = true;
function applyDarkMode() {
if (!enabled) return;
// Create style element if it doesn't exist
var style = document.getElementById('universal-dark-mode-style');
if (!style) {
style = document.createElement('style');
style.id = 'universal-dark-mode-style';
document.head.appendChild(style);
}
// Dark mode CSS - inverts colors but preserves images/video
style.textContent = '
/* Invert everything except media */
html {
filter: invert(1) hue-rotate(180deg) !important;
background: #1a1a2e !important;
}
/* Restore images, videos, iframes, canvas */
img, video, iframe, canvas, svg, picture, [style*="background-image"] {
filter: invert(1) hue-rotate(180deg) !important;
}
/* Preserve specific elements that should not be inverted */
.no-dark-mode, .no-dark-mode *,
[data-theme="light"], [data-theme="light"],
.ace_editor, .ace_editor *,
.CodeMirror, .CodeMirror *,
.monaco-editor, .monaco-editor *,
.markdown-body pre, .markdown-body pre *,
.highlight, .highlight *,
pre code, pre code * {
filter: none !important;
}
/* Fix common UI elements */
.modal, .popup, .dropdown-menu, .tooltip, .popover {
filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
}
/* Scrollbars */
::-webkit-scrollbar { background: #1a1a2e !important; }
::-webkit-scrollbar-thumb { background: #444 !important; }
::-webkit-scrollbar-thumb:hover { background: #555 !important; }
/* Selection */
::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
';
}
function removeDarkMode() {
var style = document.getElementById('universal-dark-mode-style');
if (style) style.remove();
}
// Toggle with Alt+Shift+D
document.addEventListener('keydown', function(e) {
if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
enabled = !enabled;
if (enabled) {
applyDarkMode();
console.log('[Universal Dark Mode] Enabled');
} else {
removeDarkMode();
console.log('[Universal Dark Mode] Disabled');
}
}
});
// Apply on load
applyDarkMode();
// Re-apply on dynamic content
var observer = new MutationObserver(function(mutations) {
if (enabled && !document.getElementById('universal-dark-mode-style')) {
applyDarkMode();
}
});
observer.observe(document.head, { childList: true });
console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');
})();
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

Skip to content
prove weak-head reduction weakening#39

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

 Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and
privacy statement. We’ll occasionally send you account related emails.

Already on GitHub?
Sign in
to your account

 Open

arthurpaulino
wants to merge
1
commit into

base:master
Choose a base branch

from

 Open


prove weak-head reduction weakening
#39
 Changes from all commits
Commits

Show all changes


1 commit


Select commit


File filter

Filter by extension
Filter by extension
Conversations

Failed to load comments. 
Loading
Jump to

Jump to file


Failed to load files. 
Loading
 Diff view

 Diff view


60 changes: 59 additions & 1 deletion
Lean4Lean/Experimental/SExpr.lean

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -536,6 +536,42 @@ def _root_.Lean4Lean.Pattern.Check.defeqsS {p : Pattern}
 | .true => []
 | .defeq a b rest => (a.applyS m1 m2, b.applyS m1 m2) :: rest.defeqsS m1 m2

theorem _root_.Lean4Lean.Pattern.RHS.lift'_applyS {p : Pattern} {m1 m2}
 (r : p.RHS) :
 (r.applyS m1 m2).lift' ρ = r.applyS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | fixed c h =>
 simp only [Pattern.RHS.applyS]
 rw [ClosedN.lift'_eq (h.mkS.instL) (by trivial)]
 | var => rfl
 | app _ _ ihf iha => simp only [Pattern.RHS.applyS, SExpr.lift', ihf, iha]

theorem _root_.Lean4Lean.Pattern.MatchesS.lift'
 (H : _root_.Lean4Lean.Pattern.MatchesS p e m1 m2) :
 ∃ m2', _root_.Lean4Lean.Pattern.MatchesS p (e.lift' ρ) m1 m2' ∧
 ∀ path, m2' path = (m2 path).lift' ρ := by
 induction H with
 | const => exact ⟨nofun, .const, nofun⟩
 | @var _ fn _ _ arg _ ih =>
 obtain ⟨g, hg, ih⟩ := ih
 rw [show (fn.app arg).lift' ρ = (fn.lift' ρ).app (arg.lift' ρ) from rfl]
 exact ⟨(·.elim (arg.lift' ρ) g), .var (a' := arg.lift' ρ) hg,
 fun | none => rfl | some path => ih path⟩
 | app _ _ ihf iha =>
 obtain ⟨gf, hgf, ihf⟩ := ihf
 obtain ⟨ga, hga, iha⟩ := iha
 exact ⟨Sum.elim gf ga, .app hgf hga,
 fun path => by cases path <;> simp [ihf, iha]⟩

theorem _root_.Lean4Lean.Pattern.Check.defeqsS_lift' {p : Pattern} {m1 m2}
 (r : p.Check) :
 (r.defeqsS m1 m2).map (Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)) =
 r.defeqsS m1 fun path => (m2 path).lift' ρ := by
 induction r with
 | true => rfl
 | defeq a b rest ih =>
 simp [Pattern.Check.defeqsS, Pattern.RHS.lift'_applyS, ih]

section
set_option hygiene false

Expand DownExpand Up@@ -960,7 +996,29 @@ theorem WHRed.weak' (W : Ctx.Lift' ρ Γ Γ') :
 Γ ⊢ e1 ⤳ e2 → Γ' ⊢ e1.lift' ρ ⤳ e2.lift' ρ
 | .app h1 => .app (h1.weak' W)
 | .beta => by rw [SExpr.lift'_inst_hi]; exact .beta
 | .extra h1 h2 h3 h4 => sorry
 | @extra _ _ p r e m1 m2 dfs h1 h2 h3 h4 => by
 obtain ⟨m2', hm, heq⟩ := h2.lift' (ρ := ρ)
 have heq' : m2' = fun path => (m2 path).lift' ρ := funext heq
 subst m2'
 let liftPair := Prod.map (SExpr.lift' · ρ) (SExpr.lift' · ρ)
 let dfs' := dfs.map fun x => (x.1.lift' ρ, liftPair x.2)
 rw [Pattern.RHS.lift'_applyS]
 refine .extra h1 hm (dfs := dfs') ?_ ?_
 · rw [← Pattern.Check.defeqsS_lift' (ρ := ρ), ← h3]
 unfold dfs'
 rw [List.map_map]
 simp [liftPair, Function.comp_def]
 · intro a b A hab
 obtain ⟨x, hx, hxeq⟩ := List.mem_map.1 hab
 obtain ⟨A', a', b'⟩ := x
 have hw := (h4 a' b' A' hx).weak' W
 have hA := congrArg Prod.fst hxeq
 have hp := congrArg Prod.snd hxeq
 have ha := congrArg Prod.fst hp
 have hb := congrArg Prod.snd hp
 dsimp [liftPair] at hA ha hb
 rw [← hA, ← ha, ← hb]
 exact hw

theorem WHRed.weakU_inv (W : Ctx.Lift' ρ Γ Γ') (H : Γ' ⊢ e1.lift' ρ ⤳ e2') :
 ∃ e2, e2' = e2.lift' ρ ∧ Γ ⊢ e1 ⤳ e2 := by
Expand Down