Theorems · Theorem · order theory
compl_compl_himp_distrib
∀ {α : Type u_2} [inst : HeytingAlgebra α] (a b : α), (a ⇨ b)ᶜᶜ = aᶜᶜ ⇨ bᶜᶜ- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- Compl.complstatement and proof · cited by 2,925
- le_antisymmproof · cited by 2,068
- HImp.himpstatement and proof · cited by 153
- HeytingAlgebrastatement and proof · cited by 108
- le_himp_iffproof · cited by 19
- le_compl_iff_disjoint_rightproof · cited by 10
- compl_antiproof · cited by 8
- himp_inf_leproof · cited by 6
- compl_sup_distribproof · cited by 5
- le_compl_commproof · cited by 4
- compl_compl_inf_distribproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Heyting.IsRegular.himpproof · cited by 0