Theorems · Theorem · order theory
le_himp_iff
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] {a b c : α}, a ≤ b ⇨ c ↔ a ⊓ b ≤ cp → q → r ↔ p ∧ q → r
- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- GeneralizedHeytingAlgebra
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.
- HImp.himpstatement · cited by 153
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- GeneralizedHeytingAlgebra.le_himp_iffproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- disjoint_compl_leftproof · cited by 17
- le_compl_iff_disjoint_rightproof · cited by 10
- himp_inf_leproof · cited by 6
- himp_selfproof · cited by 6
- le_himpproof · cited by 5
- himp_eq_top_iffproof · cited by 5
- le_himp_iff'proof · cited by 4
- himp_le_himp_leftproof · cited by 4
- top_himpproof · cited by 2
- inf_himpproof · cited by 2
- inf_himp_leproof · cited by 2
- himp_le_himp_rightproof · cited by 2