Theorems · Theorem · order theory
add_tsub_cancel_of_le
∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
[inst_4 : Sub α] [OrderedSub α] {a b : α}, a ≤ b → a + (b - a) = b- Cited by
- 79 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- AddLeftMonostatement and proof · cited by 687
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
- le_add_tsubproof · cited by 14
- add_tsub_le_leftproof · cited by 1
Cited by79
Results whose statement or proof uses this declaration.
- tsub_add_cancel_of_leproof · cited by 112
- add_le_of_le_tsub_left_of_leproof · cited by 7
- Complex.exp_boundproof · cited by 6
- exists_prime_orderOf_dvd_cardproof · cited by 5
- tsub_add_tsub_cancelproof · cited by 5
- PNat.factorMultiset_le_iffproof · cited by 5
- AddLECancellable.add_tsub_assoc_of_leproof · cited by 5
- AddLECancellable.tsub_lt_iff_leftproof · cited by 4
- AddLECancellable.tsub_tsub_cancel_of_leproof · cited by 4
- Finsupp.finite_of_nat_weight_leproof · cited by 3
- CompositionAsSet.blocks_partial_sumproof · cited by 3
- LinearMap.exists_isNilRegular_of_finrank_le_cardproof · cited by 3