Theorems · Theorem · order theory

LinearPMap.supSpanSingleton.congr_simp

∀ {E : Type u_4} [inst : AddCommGroup E] {F : Type u_5} [inst_1 : AddCommGroup F] {K : Type u_7} {L : Type u_8}
  [inst_2 : DivisionRing K] [inst_3 : DivisionRing L] {σ : K →+* L} [inst_4 : Module K E] [inst_5 : Module L F]
  (f f_1 : E →ₛₗ.[σ] F) (e_f : f = f_1) (x x_1 : E) (e_x : x = x_1) (y y_1 : F),
  y = y_1 → ∀ (hx : x ∉ f.domain), f.supSpanSingleton x y hx = f_1.supSpanSingleton x_1 y_1 ⋯

Defined in

Mathlib.Algebra.Order.Module.HahnEmbedding

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupDivisionRingDivisionRingModuleModule