Theorems · Theorem · number theory
Nat.ModEq.of_natCast
∀ {M : Type u_1} [inst : AddCommMonoidWithOne M] [CharZero M] {a b n : ℕ}, ↑a ≡ ↑b [PMOD ↑n] → a ≡ b [MOD n]Alias of the forward direction of AddCommGroup.natCast_modEq_natCast.
- Defined in
- Mathlib.Data.Nat.ModEq
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidWithOneCharZero
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CharZerostatement and proof · cited by 932
- Nat.ModEqstatement · cited by 225
- AddCommGroup.ModEqstatement · cited by 107
- AddCommMonoidWithOnestatement and proof · cited by 42
- AddCommGroup.natCast_modEq_natCastproof · cited by 1
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