refactor: Linting substrings

This commit is contained in:
jstoobysmith 2024-07-12 16:22:06 -04:00
parent cee38b7be8
commit ac1132c7ca
40 changed files with 133 additions and 132 deletions

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@ -34,7 +34,7 @@ open SpaceTime
/-- The Higgs potential of the form `- μ² * |φ|² + 𝓵 * |φ|⁴`. -/
@[simp]
def potential (μ2 𝓵 : ) (φ : HiggsField) (x : SpaceTime) : :=
def potential (μ2 𝓵 : ) (φ : HiggsField) (x : SpaceTime) : :=
- μ2 * ‖φ‖_H ^ 2 x + 𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x
/-!
@ -94,7 +94,7 @@ lemma snd_term_nonneg (φ : HiggsField) (x : SpaceTime) :
and_self]
lemma as_quad (μ2 𝓵 : ) (φ : HiggsField) (x : SpaceTime) :
𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x + (- μ2 ) * ‖φ‖_H ^ 2 x + (- potential μ2 𝓵 φ x) = 0 := by
𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x + (- μ2) * ‖φ‖_H ^ 2 x + (- potential μ2 𝓵 φ x) = 0 := by
simp only [normSq, neg_mul, potential, neg_add_rev, neg_neg]
ring
@ -237,7 +237,7 @@ lemma IsMinOn_iff_of_μSq_nonpos {μ2 : } (hμ2 : μ2 ≤ 0) :
have h0 := isMinOn_univ_iff.mp h 0
have h1 := bounded_below_of_μSq_nonpos h𝓵 hμ2 φ x
simp only at h0
rw [(eq_bound_iff_of_μSq_nonpos h𝓵 hμ2 0 0 ).mpr (by rfl)] at h0
rw [(eq_bound_iff_of_μSq_nonpos h𝓵 hμ2 0 0).mpr (by rfl)] at h0
exact (Real.partialOrder.le_antisymm _ _ h1 h0).symm
· exact eq_bound_IsMinOn_of_μSq_nonpos h𝓵 hμ2 φ x