Theorems · Theorem · order theory
compl_bot
∀ {α : Type u_2} [inst : HeytingAlgebra α], ⊥ᶜ = ⊤- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- HeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- Compl.complstatement · cited by 2,925
- HeytingAlgebrastatement and proof · cited by 108
- himp_botproof · cited by 9
- himp_selfproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Set.compl_emptyproof · cited by 33
- Finset.compl_emptyproof · cited by 5
- BooleanSubalgebra.top_memproof · cited by 5
- Set.Intersecting.is_max_iff_card_eqproof · cited by 2
- BooleanSubalgebra.mem_closure_iff_sup_sdiffproof · cited by 1
- ne_compl_selfproof · cited by 1
- Heyting.isRegular_botproof · cited by 0
- Heyting.isRegular_topproof · cited by 0