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Theorems · Theorem · group theory

AddEquiv.map_add

∀ {M : Type u_4} {N : Type u_5} [inst : Add M] [inst_1 : Add N] (f : M ≃+ N) (x y : M), f (x + y) = f x + f y

An additive isomorphism preserves addition.

Defined in
Mathlib.Algebra.Group.Equiv.Defs
Cited by
4 results in Mathlib
Foundations
Depth 18 from the axioms · uses Quot.sound
Assumes
AddAdd
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CochainComplex.HomComplex.Cochain.fromSingleMk_add · cited by 1Cochain.fromSingleMk_addCochainComplex.HomComplex.Cochain.toSingleMk_add · cited by 1Cochain.toSingleMk_addCategoryTheory.InjectiveResolution.extEquivCohomologyClass_add · cited by 0InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add · cited by 0ProjectiveResolution.extE…DFunLike.coe · cited by 62936DFunLike.coeAddEquiv · cited by 1087AddEquivmap_add · cited by 964map_addAddEquiv.map_addCITED BYCITES

Cites3

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Cited by4

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