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refactor: pass at removing double spaces

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jstoobysmith 2024-07-12 10:36:39 -04:00
parent 1fe51b2e04
commit 1133b883f3
19 changed files with 121 additions and 121 deletions
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6
HepLean/Mathematics/LinearMaps.lean
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@ -77,7 +77,7 @@ def mk₂ (f : V × V → ℚ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S,
exact congrArg (HMul.hMul a) (swap T S)
}
map_smul' := fun a S => LinearMap.ext fun T => map_smul a S T
map_add' := fun S1 S2 => LinearMap.ext fun T => map_add S1 S2 T
map_add' := fun S1 S2 => LinearMap.ext fun T => map_add S1 S2 T
swap' := swap
lemma map_smul₁ (f : BiLinearSymm V) (a : ℚ) (S T : V) : f (a • S) T = a * f S T := by
@ -99,7 +99,7 @@ lemma map_add₂ (f : BiLinearSymm V) (S : V) (T1 T2 : V) :
rw [f.swap, f.map_add₁, f.swap T1 S, f.swap T2 S]
/-- Fixing the second input vectors, the resulting linear map. -/
def toLinear₁ (f : BiLinearSymm V) (T : V) : V →ₗ[ℚ] ℚ where
def toLinear₁ (f : BiLinearSymm V) (T : V) : V →ₗ[ℚ] ℚ where
toFun S := f S T
map_add' S1 S2 := map_add₁ f S1 S2 T
map_smul' a S := by
@ -166,7 +166,7 @@ end HomogeneousCubic
/-- The structure of a symmetric trilinear function. -/
structure TriLinearSymm (V : Type) [AddCommMonoid V] [Module ℚ V] extends
V →ₗ[ℚ] V →ₗ[ℚ] V →ₗ[ℚ] ℚ where
swap₁' : ∀ S T L, toFun S T L = toFun T S L
swap₁' : ∀ S T L, toFun S T L = toFun T S L
swap₂' : ∀ S T L, toFun S T L = toFun S L T
namespace TriLinearSymm