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lemma: Contract with unitTensor

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jstoobysmith 2024-11-15 15:46:08 +00:00
parent c02f84c45e
commit 5603a67642
3 changed files with 211 additions and 1 deletions
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20
HepLean/Tensors/OverColor/Discrete.lean
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@ -276,6 +276,26 @@ lemma rep_iso_hom_inv_apply (x y : Rep k G) (f : x ≅ y) (i : y) :
change (f.inv ≫ f.hom).hom i = i
simp
lemma rep_iso_apply_iff (x y : Rep k G) (f : x ≅ y) (i : x) (j : y) :
f.hom.hom i = j ↔ i = f.inv.hom j := by
apply Iff.intro
· intro a
subst a
simp_all only [rep_iso_inv_hom_apply]
· intro a
subst a
exact rep_iso_hom_inv_apply x y f j
lemma rep_iso_inv_apply_iff (x y : Rep k G) (f : x ≅ y) (i : y) (j : x) :
f.inv.hom i = j ↔ i = f.hom.hom j := by
apply Iff.intro
· intro a
subst a
simp_all only [rep_iso_hom_inv_apply]
· intro a
subst a
simp_all only [rep_iso_inv_hom_apply]
end
end Discrete
end OverColor