Theorems · Theorem · order theory
tsub_eq_iff_eq_add_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 c : α} [AddLeftReflectLE α], b ≤ a → (a - b = c ↔ a = c + b)- Cited by
- 12 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- AddLeftReflectLEstatement and proof · cited by 119
- Contravariant.AddLECancellableproof · cited by 45
- AddLECancellable.tsub_eq_iff_eq_add_of_leproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.hasseDeriv_monomialproof · cited by 5
- CompositionAsSet.card_boundaries_eq_succ_lengthproof · cited by 4
- Finset.mem_upShadow_iff_exists_mem_card_add_oneproof · cited by 2
- IsCauSeq.of_abv_leproof · cited by 2
- IsCauSeq.series_ratio_testproof · cited by 1
- pow_pow_modEq_oneproof · cited by 1
- C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sumproof · cited by 1
- Finset.mem_shadow_iff_exists_mem_card_add_oneproof · cited by 1
- ZMod.eq_one_or_isUnit_sub_oneproof · cited by 1
- Finset.mem_upShadow_iterate_iff_exists_mem_card_addproof · cited by 0
- MvPolynomial.coeff_pderivproof · cited by 0
- Finset.mem_shadow_iterate_iff_exists_mem_card_addproof · cited by 0