Theorems · Theorem · logic and foundations
Ordinal.div_add_mod
∀ (a b : Ordinal.{u_4}), b * (a / b) + a % b = a- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Ordinal.add_sub_cancel_of_leproof · cited by 14
- Ordinal.mul_div_leproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Ordinal.mod_ltproof · cited by 5
- Ordinal.mul_eq_right_iff_opow_omega0_dvdproof · cited by 2
- Ordinal.mul_add_mod_mulproof · cited by 1
- Ordinal.CNF.foldrproof · cited by 1
- Ordinal.dvd_of_mod_eq_zeroproof · cited by 1
- Ordinal.mod_mod_of_dvdproof · cited by 1
- Ordinal.sub_omega0_opow_log_ltproof · cited by 1
- Ordinal.lt_mul_iffproof · cited by 0
- Ordinal.natCast_modproof · cited by 0
- Ordinal.two_opow_log_addproof · cited by 0