Theorems · Theorem · number theory
ZMod.coe_int_mul_inv_eq_one
∀ {n : ℕ} {x : ℤ}, IsCoprime x ↑n → ↑x * (↑x)⁻¹ = 1- Defined in
- Mathlib.Data.ZMod.Units
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.cast_zeroproof · cited by 1,870
- ZModstatement and proof · cited by 1,024
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- Int.cast_oneproof · cited by 371
- IsCoprimestatement and proof · cited by 321
- Int.cast_negproof · cited by 224
- ZMod.valproof · cited by 159
- ZMod.natCast_zmod_valproof · cited by 29
- Int.isCoprime_iff_gcd_eq_oneproof · cited by 16
- Int.isUnit_eq_one_orproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ZMod.unitOfIsCoprimeproof · cited by 4
- ZMod.coe_int_mul_val_invproof · cited by 1
- ZMod.coe_int_inv_mul_eq_oneproof · cited by 0