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Theorems · Theorem · order theory

AddLECancellable.tsub_add_eq_add_tsub

∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
  [inst_4 : Sub α] [OrderedSub α] {a b c : α}, AddLECancellable b → b ≤ a → a - b + c = a + c - b
Defined in
Mathlib.Algebra.Order.Sub.Unbundled.Basic
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
AddCommSemigroupPartialOrderExistsAddOfLEAddLeftMonoSubOrderedSub
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Around this declaration

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

tsub_add_eq_add_tsub · cited by 23tsub_add_eq_add_tsubAddLECancellable.tsub_add_tsub_comm · cited by 1AddLECancellable.tsub_add…PartialOrder · cited by 6410PartialOrderadd_comm · cited by 1535add_commAddLeftMono · cited by 687AddLeftMonoExistsAddOfLE · cited by 330ExistsAddOfLEOrderedSub · cited by 236OrderedSubAddCommSemigroup · cited by 178AddCommSemigroupAddLECancellable · cited by 87AddLECancellableAddLECancellable.add_tsub_assoc_of_le · cited by 5AddLECancellable.add_tsub…AddLECancellable.tsub_add_eq_…CITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.