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Theorems · Theorem · order theory

add_tsub_cancel_iff_le

∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
  [OrderedSub α] {a b : α}, a + (b - a) = b ↔ a ≤ b
Defined in
Mathlib.Algebra.Order.Sub.Basic
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidPartialOrderCanonicallyOrderedAddSubOrderedSub
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Around this declaration

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

tsub_add_cancel_iff_le · cited by 1tsub_add_cancel_iff_lePNat.one_add_natPred · cited by 1PNat.one_add_natPredAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderOrderedSub · cited by 236OrderedSubCanonicallyOrderedAdd · cited by 229CanonicallyOrderedAddadd_tsub_cancel_of_le · cited by 79add_tsub_cancel_of_lele_iff_exists_add · cited by 16le_iff_exists_addadd_tsub_cancel_iff_leCITED BYCITES

Cites6

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.