Theorems · Theorem · commutative algebra

LinearMap.mk.congr_simp

∀ {R : Type u_14} {S : Type u_15} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {M : Type u_16}
  {M₂ : Type u_17} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module S M₂]
  (toAddHom toAddHom_1 : M →ₙ+ M₂) (e_toAddHom : toAddHom = toAddHom_1)
  (map_smul' : ∀ (m : R) (x : M), toAddHom.toFun (m • x) = σ m • toAddHom.toFun x),
  { toAddHom := toAddHom, map_smul' := map_smul' } = { toAddHom := toAddHom_1, map_smul' := ⋯ }

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

27 results in Mathlib

Foundations

Depth 17 from the axioms · uses no axioms

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule