Theorems · Theorem · number theory
ZMod.intCast_eq_iff
∀ (p : ℕ) (n : ℤ) (z : ZMod p) [NeZero p], ↑n = z ↔ ∃ k, n = ↑z.val + ↑p * k
- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- MulZeroClass.zero_mulproof · cited by 1,625
- ZModstatement and proof · cited by 1,024
- Int.cast_natCastproof · cited by 393
- ZMod.valstatement and proof · cited by 159
- Int.cast_addproof · cited by 124
- Int.cast_mulproof · cited by 113
- ZMod.castproof · cited by 87
- ZMod.natCast_valproof · cited by 27
- ZMod.natCast_selfproof · cited by 15
- ZMod.cast_idproof · cited by 7
- ZMod.val_intCastproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclic.unique_zpow_zmodproof · cited by 0
- IsAddCyclic.unique_zsmul_zmodproof · cited by 0