Theorems · Theorem · linear algebra

Submodule.quotientPiLift.congr_simp

∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] {Ms : ι → Type u_3} [inst_1 : (i : ι) → AddCommGroup (Ms i)]
  [inst_2 : (i : ι) → Module R (Ms i)] {Ns : ι → Type u_5} [inst_3 : (i : ι) → AddCommGroup (Ns i)]
  [inst_4 : (i : ι) → Module R (Ns i)] (p : (i : ι) → Submodule R (Ms i)) (f f_1 : (i : ι) → Ms i →ₗ[R] Ns i)
  (e_f : f = f_1) (hf : ∀ (i : ι), p i ≤ (f i).ker), Submodule.quotientPiLift p f hf = Submodule.quotientPiLift p f_1 ⋯

Defined in

Mathlib.LinearAlgebra.Quotient.Pi

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule