Theorems · Theorem · order theory
sup_lt_sup_of_lt_of_inf_le_inf
∀ {α : Type u_1} [inst : Lattice α] [IsModularLattice α] {x y z : α}, y < x → x ⊓ z ≤ y ⊓ z → y ⊔ z < x ⊔ z- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- LatticeIsModularLattice
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.
- le_of_ltproof · cited by 1,175
- Latticestatement and proof · cited by 916
- le_of_eqproof · cited by 366
- lt_of_le_of_neproof · cited by 230
- ne_of_ltproof · cited by 203
- IsModularLatticestatement and proof · cited by 86
- sup_le_sup_rightproof · cited by 14
- eq_of_le_of_inf_le_of_sup_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- strictMono_inf_prod_supproof · cited by 2