Theorems · Theorem · order theory
himp_bot
∀ {α : Type u_2} [inst : HeytingAlgebra α] (a : α), a ⇨ ⊥ = aᶜ- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Compl.complstatement · cited by 2,925
- HImp.himpstatement · cited by 153
- HeytingAlgebrastatement and proof · cited by 108
- HeytingAlgebra.himp_botproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- disjoint_compl_leftproof · cited by 17
- le_compl_iff_disjoint_rightproof · cited by 10
- compl_botproof · cited by 8
- map_complproof · cited by 2
- compl_le_himpproof · cited by 2
- isGreatest_complproof · cited by 1
- himp_complproof · cited by 1
- bihimp_botproof · cited by 0
- bot_bihimpproof · cited by 0