Mathlib Map

Theorems · Theorem · number theory

WithZero.coe_le_coe

∀ {α : Type u_1} [inst : LE α] {a b : α}, ↑a ≤ ↑b ↔ a ≤ b
Defined in
Mathlib.Algebra.Order.GroupWithZero.Canonical
Cited by
8 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered · cited by 4LinearOrderedCommGroupWit…LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete_of_ne_zero · cited by 2LinearOrderedCommGroupWit…WithZero.le_ofAdd_of_toAdd_unzero_le · cited by 1WithZero.le_ofAdd_of_toAd…LaurentSeries.exists_Polynomial_intValuation_lt · cited by 1LaurentSeries.exists_Poly…WithZero.toAdd_unzero_le_of_lt_ofAdd · cited by 1WithZero.toAdd_unzero_le_…WithZero.addLeftMono · cited by 1WithZero.addLeftMonoWithZero.coe_le_one · cited by 0WithZero.coe_le_oneWithZero.one_le_coe · cited by 0WithZero.one_le_coeWithZero · cited by 586WithZeroWithZero.coe · cited by 186WithZero.coeWithBot.coe_le_coe · cited by 76WithBot.coe_le_coeWithZero.coe_le_coeCITED BYCITES

Cites3

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

Cited by8

Results whose statement or proof uses this declaration.