Theorems · Theorem · commutative algebra

IsHausdorff.funext

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {N : Type u_5} [inst_1 : AddCommGroup N] [inst_2 : Module R N]
  {M : Type u_6} [IsHausdorff I N] {f g : M → N},
  (∀ (n : ℕ) (m : M), Submodule.Quotient.mk (f m) = Submodule.Quotient.mk (g m)) → f = g

Defined in: Mathlib.RingTheory.AdicCompletion.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsHausdorff

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement · cited by 9,680
Submodulestatement · cited by 7,192
Idealstatement and proof · cited by 4,748
HasQuotient.Quotientstatement · cited by 2,301
Submodule.Quotient.mkstatement and proof · cited by 184
IsHausdorffstatement and proof · cited by 37
IsHausdorff.eq_iff_smodEqproof · cited by 6

Cited by1

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IsAdicComplete.eq_liftproof · cited by 0