Theorems · Theorem · order theory
IsOrderedVAdd.vadd_le_vadd_left
∀ {G : Type u_3} {P : Type u_4} {inst : LE G} {inst_1 : LE P} {inst_2 : VAdd G P} [self : IsOrderedVAdd G P] (a b : P),
a ≤ b → ∀ (c : G), c +ᵥ a ≤ c +ᵥ b- Defined in
- Mathlib.Algebra.Order.AddTorsor
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- IsOrderedVAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- HVAdd.hVAddstatement · cited by 1,820
- VAddstatement and proof · cited by 616
- IsOrderedVAddstatement and proof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- VAdd.vadd_lt_vadd_of_lt_of_leproof · cited by 2
- IsOrderedVAdd.vadd_le_vaddproof · cited by 1
- Monotone.vaddproof · cited by 1
- VAdd.vadd_lt_vadd_of_le_of_ltproof · cited by 0