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Adopt lemma as the default keyword

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Convert every theorem to lemma (mathlib's default) except the headline results a
reader of each module seeks out: analyze_correct (Forward/Sign/Constant),
aFix_eq/aFix_le (Fixedpoint), trace (Language), and Stmt.cfg_sufficient
(Language/Properties). lemma and theorem are interchangeable keywords, so no
references change.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-25 13:59:08 -05:00
parent 5c9c8ac55c
commit e2df847139
20 changed files with 143 additions and 143 deletions
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30
lean/Spa/Language/Graphs.lean
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@@ -41,10 +41,10 @@ def map (f : α → β) (g : GGraph α) : GGraph β where
inputs := g.inputs
outputs := g.outputs
@[simp] theorem map_size (f : α → β) (g : GGraph α) : (g.map f).size = g.size := rfl
@[simp] theorem map_edges (f : α → β) (g : GGraph α) : (g.map f).edges = g.edges := rfl
@[simp] theorem map_inputs (f : α → β) (g : GGraph α) : (g.map f).inputs = g.inputs := rfl
@[simp] theorem map_outputs (f : α → β) (g : GGraph α) : (g.map f).outputs = g.outputs := rfl
@[simp] lemma map_size (f : α → β) (g : GGraph α) : (g.map f).size = g.size := rfl
@[simp] lemma map_edges (f : α → β) (g : GGraph α) : (g.map f).edges = g.edges := rfl
@[simp] lemma map_inputs (f : α → β) (g : GGraph α) : (g.map f).inputs = g.inputs := rfl
@[simp] lemma map_outputs (f : α → β) (g : GGraph α) : (g.map f).outputs = g.outputs := rfl
def comp (g₁ g₂ : GGraph α) : GGraph α where
size := g₁.size + g₂.size
@@ -79,9 +79,9 @@ def loop (g : GGraph (List β)) : GGraph (List β) where
inputs := [g.loopIn]
outputs := [g.loopOut]
@[simp] theorem loop_inputs (g : GGraph (List β)) : (loop g).inputs = [g.loopIn] := rfl
@[simp] lemma loop_inputs (g : GGraph (List β)) : (loop g).inputs = [g.loopIn] := rfl
@[simp] theorem loop_outputs (g : GGraph (List β)) : (loop g).outputs = [g.loopOut] := rfl
@[simp] lemma loop_outputs (g : GGraph (List β)) : (loop g).outputs = [g.loopOut] := rfl
def skipto (g₁ g₂ : GGraph α) : GGraph α where
size := g₁.size + g₂.size
@@ -101,10 +101,10 @@ def singleton (a : α) : GGraph α where
def wrap (g : GGraph (List β)) : GGraph (List β) :=
singleton [] ⤳ g ⤳ singleton []
@[simp] theorem map_singleton (f : α → β) (a : α) :
@[simp] lemma map_singleton (f : α → β) (a : α) :
(singleton a).map f = singleton (f a) := rfl
@[simp] theorem map_comp (f : α → β) (g₁ g₂ : GGraph α) :
@[simp] lemma map_comp (f : α → β) (g₁ g₂ : GGraph α) :
(g₁ ∙ g₂).map f = g₁.map f ∙ g₂.map f := by
rcases g₁ with ⟨n₁, nd₁, e₁, i₁, o₁⟩; rcases g₂ with ⟨n₂, nd₂, e₂, i₂, o₂⟩
simp only [GGraph.map, GGraph.comp]
@@ -112,7 +112,7 @@ def wrap (g : GGraph (List β)) : GGraph (List β) :=
funext i
refine Fin.addCases ?_ ?_ i <;> intro j <;> simp [Fin.append_left, Fin.append_right]
@[simp] theorem map_link (f : α → β) (g₁ g₂ : GGraph α) :
@[simp] lemma map_link (f : α → β) (g₁ g₂ : GGraph α) :
(g₁ ⤳ g₂).map f = g₁.map f ⤳ g₂.map f := by
rcases g₁ with ⟨n₁, nd₁, e₁, i₁, o₁⟩; rcases g₂ with ⟨n₂, nd₂, e₂, i₂, o₂⟩
simp only [GGraph.map, GGraph.link]
@@ -120,7 +120,7 @@ def wrap (g : GGraph (List β)) : GGraph (List β) :=
funext i
refine Fin.addCases ?_ ?_ i <;> intro j <;> simp [Fin.append_left, Fin.append_right]
@[simp] theorem map_loop (h : β → γ) (g : GGraph (List β)) :
@[simp] lemma map_loop (h : β → γ) (g : GGraph (List β)) :
(loop g).map (List.map h) = loop (g.map (List.map h)) := by
rcases g with ⟨n, nd, e, i, o⟩
simp only [GGraph.map, GGraph.loop]
@@ -128,7 +128,7 @@ def wrap (g : GGraph (List β)) : GGraph (List β) :=
funext i
refine Fin.addCases ?_ ?_ i <;> intro j <;> simp [Fin.append_left, Fin.append_right]
@[simp] theorem map_wrap (h : β → γ) (g : GGraph (List β)) :
@[simp] lemma map_wrap (h : β → γ) (g : GGraph (List β)) :
(wrap g).map (List.map h) = wrap (g.map (List.map h)) := by
simp [GGraph.wrap, GGraph.map_link, GGraph.map_singleton]
@@ -136,20 +136,20 @@ variable (g : GGraph α)
def indices : List g.Index := List.finRange g.size
theorem mem_indices (idx : g.Index) : idx ∈ g.indices :=
lemma mem_indices (idx : g.Index) : idx ∈ g.indices :=
List.mem_finRange idx
theorem nodup_indices : g.indices.Nodup :=
lemma nodup_indices : g.indices.Nodup :=
List.nodup_finRange g.size
def predecessors (idx : g.Index) : List g.Index :=
g.indices.filter (fun idx' => (idx', idx) ∈ g.edges)
theorem mem_predecessors_of_edge {idx₁ idx₂ : g.Index}
lemma mem_predecessors_of_edge {idx₁ idx₂ : g.Index}
(h : (idx₁, idx₂) ∈ g.edges) : idx₁ ∈ g.predecessors idx₂ :=
List.mem_filter.mpr ⟨g.mem_indices idx₁, by simpa using h⟩
theorem edge_of_mem_predecessors {idx₁ idx₂ : g.Index}
lemma edge_of_mem_predecessors {idx₁ idx₂ : g.Index}
(h : idx₁ ∈ g.predecessors idx₂) : (idx₁, idx₂) ∈ g.edges := by
simpa using (List.mem_filter.mp h).2