Theorems · Theorem · general topology
PiNat.res_eq_res
∀ {α : Type u_2} {x y : ℕ → α} {n : ℕ}, PiNat.res x n = PiNat.res y n ↔ ∀ ⦃m : ℕ⦄, m < n → x m = y mThe restrictions of x and y to n are equal if and only if x m = y m for all m < n.
- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.transproof · cited by 370
- PiNat.resstatement and proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- PiNat.cylinder_eq_resproof · cited by 1
- PiNat.res_injectiveproof · cited by 1