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Jun 24, 2026
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refactor(Phonology/Autosegmental): golf concat proofs with grind #751

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refactor(Phonology/Autosegmental): golf concat proofs with grind
hawkrobe Jun 24, 2026
4c9799d
Merge branch 'main' into autoseg-graph-golf
hawkrobe Jun 24, 2026
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11 changes: 3 additions & 8 deletions Linglib/Phonology/Autosegmental/Graph.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -269,8 +269,8 @@ theorem concat_assoc (A B C : Graph α β) :
(A.concat B).concat C = A.concat (B.concat C) :=
Graph.ext (LabeledTuple.concat_assoc A.upper B.upper C.upper)
(LabeledTuple.concat_assoc A.lower B.lower C.lower)
(by simp only [links_concat, upper_concat, lower_concat, LabeledTuple.concat_len,
Finset.image_union, Finset.image_image, shiftLink_comp]; rw [Finset.union_assoc])
(by grind [links_concat, upper_concat, lower_concat, LabeledTuple.concat_len,
Finset.image_union, Finset.image_image, shiftLink_comp])

/-! #### Planarity preservation ([jardine-heinz-2015] Theorem 4) -/

Expand All @@ -291,12 +291,7 @@ theorem isPlanar_concat {A B : Graph α β} (hAib : A.InBounds) (hA : A.IsPlanar
/-- Concatenation preserves in-bounds. -/
theorem inBounds_concat {A B : Graph α β}
(hA : A.InBounds) (hB : B.InBounds) : (A.concat B).InBounds := by
rintro p hp
simp only [links_concat, Finset.mem_union, Finset.mem_image, upper_concat, lower_concat,
LabeledTuple.concat_len] at hp ⊢
obtain hp | ⟨q, hq, rfl⟩ := hp
· have := hA p hp; omega
· have := hB q hq; simp only [shiftLink]; omega
grind [InBounds, links_concat, upper_concat, lower_concat, LabeledTuple.concat_len, shiftLink]

end Graph

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