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Theorems · Theorem · logic and foundations

Ordinal.div_eq_zero_of_lt

∀ {a b : Ordinal.{u_4}}, a < b → a / b = 0
Defined in
Mathlib.SetTheory.Ordinal.Arithmetic
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ordinal.mod_eq_of_lt · cited by 2Ordinal.mod_eq_of_ltOrdinal.CNF.opow_mul_add · cited by 1CNF.opow_mul_addmul_one · cited by 3885mul_onezero_add · cited by 2366zero_addOrdinal · cited by 1688OrdinalOrder.succ_eq_add_one · cited by 115Order.succ_eq_add_onenonpos_iff_eq_zero · cited by 100nonpos_iff_eq_zeroLT.lt.ne_bot · cited by 26lt.ne_botOrdinal.div_le · cited by 6Ordinal.div_leOrdinal.div_eq_zero_of_ltCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.