Theorems · Theorem · general topology
PiNat.apply_eq_of_lt_firstDiff
∀ {E : ℕ → Type u_1} {x y : (n : ℕ) → E n} {n : ℕ}, n < PiNat.firstDiff x y → x n = y n- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.findproof · cited by 139
- PiNat.firstDiffstatement and proof · cited by 23
- PiNat.firstDiff_defproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- PiNat.mem_cylinder_firstDiffproof · cited by 5
- PiNat.mem_cylinder_iff_dist_leproof · cited by 4
- PiNat.apply_eq_of_dist_ltproof · cited by 3
- PiNat.mem_cylinder_iff_le_firstDiffproof · cited by 2
- PiNat.cylinder_eq_cylinder_of_le_firstDiffproof · cited by 1
- PiNat.min_firstDiff_leproof · cited by 1