Theorems · Theorem · number theory
ZMod.natCast_eq_natCast_iff
∀ (a b c : ℕ), ↑a = ↑b ↔ a ≡ b [MOD c]
- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZModstatement · cited by 1,024
- Int.cast_natCastproof · cited by 393
- Nat.ModEqstatement · cited by 225
- ZMod.intCast_eq_intCast_iffproof · cited by 11
Cited by13
Results whose statement or proof uses this declaration.
- ZMod.natCast_eq_zero_iffproof · cited by 10
- ZMod.val_coe_unit_coprimeproof · cited by 6
- ZMod.natCast_eq_natCast_iff'proof · cited by 4
- IsPGroup.card_modEq_card_fixedPointsproof · cited by 4
- ZMod.prime_ne_zeroproof · cited by 4
- PadicInt.existsUnique_mem_rangeproof · cited by 2
- IsCyclic.extproof · cited by 1
- Nat.ModEq.pow_totientproof · cited by 1
- DirichletCharacter.factorsThrough_gcdproof · cited by 1
- ZMod.eisenstein_lemma_auxproof · cited by 1
- ZMod.eq_one_or_isUnit_sub_oneproof · cited by 1
- ZMod.eq_unit_mul_divisorproof · cited by 1