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refactor: Last batch of multi-goal proofs

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jstoobysmith 2024-08-21 06:40:58 -04:00
parent b9479c904d
commit c0499483a8
43 changed files with 910 additions and 955 deletions
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12
HepLean/AnomalyCancellation/SMNu/PlusU1/QuadSolToSol.lean
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@ -101,9 +101,7 @@ def quadSolToSolInv {n : ℕ} : (PlusU1 n).Sols → (PlusU1 n).QuadSols × ℚ
lemma quadSolToSolInv_1 (S : (PlusU1 n).Sols) :
(quadSolToSolInv S).1 = S.1 := by
simp [quadSolToSolInv]
split
rfl
rfl
split <;> rfl
lemma quadSolToSolInv_α₁_α₂_zero (S : (PlusU1 n).Sols) (h : α₁ S.1 = 0) :
α₁ (quadSolToSolInv S).1 = 0 ∧ α₂ (quadSolToSolInv S).1 = 0 := by
@ -133,10 +131,10 @@ lemma quadSolToSolInv_generic (S : (PlusU1 n).Sols) (h : α₁ S.1 ≠ 0) :
lemma quadSolToSolInv_rightInverse : Function.RightInverse (@quadSolToSolInv n) quadSolToSol := by
intro S
by_cases h : α₁ S.1 = 0
rw [quadSolToSol, dif_pos (quadSolToSolInv_α₁_α₂_zero S h)]
exact quadSolToSolInv_special S h
rw [quadSolToSol, dif_neg (quadSolToSolInv_α₁_α₂_neq_zero S h)]
exact quadSolToSolInv_generic S h
· rw [quadSolToSol, dif_pos (quadSolToSolInv_α₁_α₂_zero S h)]
exact quadSolToSolInv_special S h
· rw [quadSolToSol, dif_neg (quadSolToSolInv_α₁_α₂_neq_zero S h)]
exact quadSolToSolInv_generic S h
theorem quadSolToSol_surjective : Function.Surjective (@quadSolToSol n) :=
Function.RightInverse.surjective quadSolToSolInv_rightInverse