Mathlib Map

Theorems · Theorem · number theory

WithZero.toAdd_unzero_le_of_lt_ofAdd

∀ {α : Type u_1} [inst : Preorder α] {a : WithZero (Multiplicative α)} {b : α} (ha : a ≠ 0),
  a ≤ ↑(Multiplicative.ofAdd b) → Multiplicative.toAdd (WithZero.unzero ha) ≤ b
Defined in
Mathlib.Algebra.Order.GroupWithZero.Canonical
Cited by
1 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithZero.le_ofAdd_iff · cited by 1WithZero.le_ofAdd_iffDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivPreorder · cited by 7952PreorderMultiplicative · cited by 875MultiplicativeWithZero · cited by 586WithZeroMultiplicative.ofAdd · cited by 237Multiplicative.ofAddWithZero.coe · cited by 186WithZero.coeMultiplicative.toAdd · cited by 161Multiplicative.toAddWithZero.unzero · cited by 38WithZero.unzeroWithZero.coe_unzero · cited by 17WithZero.coe_unzeroWithZero.coe_le_coe · cited by 8WithZero.coe_le_coeMultiplicative.toAdd_le · cited by 4Multiplicative.toAdd_letoAdd_ofAdd · cited by 4toAdd_ofAddWithZero.toAdd_unzero_le_of_l…CITED BYCITES

Cites13

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

Cited by1

Results whose statement or proof uses this declaration.