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Theorems · Theorem · number theory

WithZero.coe_lt_coe

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

Around this declaration

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

WithZero.exists_ne_zero_and_lt · cited by 2WithZero.exists_ne_zero_a…WithZero.lt_ofAdd_of_toAdd_unzero_lt · cited by 1WithZero.lt_ofAdd_of_toAd…LaurentSeries.exists_Polynomial_intValuation_lt · cited by 1LaurentSeries.exists_Poly…WithZero.toAdd_unzero_lt_of_lt_ofAdd · cited by 1WithZero.toAdd_unzero_lt_…WithZero.coe_lt_one · cited by 0WithZero.coe_lt_oneWithZero.one_lt_coe · cited by 0WithZero.one_lt_coeWithZero · cited by 586WithZeroWithZero.coe · cited by 186WithZero.coeWithZero.coe_lt_coeCITED BYCITES

Cites2

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

Cited by6

Results whose statement or proof uses this declaration.