Theorems · Theorem · order theory
VAdd.vadd_lt_vadd_of_lt_of_le
∀ {G : Type u_1} {P : Type u_2} [inst : Preorder G] [inst_1 : Preorder P] [inst_2 : VAdd G P] [IsOrderedCancelVAdd G P]
{a b : G} {c d : P}, a < b → c ≤ d → a +ᵥ c < b +ᵥ d- Defined in
- Mathlib.Algebra.Order.AddTorsor
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- HVAdd.hVAddstatement and proof · cited by 1,820
- le_of_ltproof · cited by 1,175
- VAddstatement and proof · cited by 616
- lt_of_le_of_ltproof · cited by 432
- lt_iff_le_not_geproof · cited by 35
- lt_of_le_not_geproof · cited by 33
- IsOrderedCancelVAddstatement and proof · cited by 31
- IsOrderedVAdd.vadd_le_vadd_leftproof · cited by 4
- IsOrderedVAdd.vadd_le_vadd_rightproof · cited by 4
- IsOrderedCancelVAdd.le_of_vadd_le_vadd_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.VAddAntidiagonal.eq_of_fst_le_fst_of_snd_le_sndproof · cited by 1
- Finset.vaddAntidiagonal_min_vadd_minproof · cited by 1