Theorems · Theorem · number theory
Nat.add_mod_add_ite
∀ (a b c : ℕ), ((a + b) % c + if c ≤ a % c + b % c then c else 0) = a % c + b % c
- Defined in
- Mathlib.Data.Nat.ModEq
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- le_antisymmproof · cited by 2,068
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- lt_of_not_geproof · cited by 374
- mul_twoproof · cited by 43
- Nat.ModEq.symmproof · cited by 29
- add_right_cancel_iffproof · cited by 19
- Nat.ModEq.addproof · cited by 7
- Nat.mod_modEqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Nat.add_mod_of_add_mod_ltproof · cited by 1
- Nat.add_mod_add_of_le_add_modproof · cited by 1