Theorems · Theorem · order theory
compl_le_compl
∀ {α : Type u_2} [inst : HeytingAlgebra α] {a b : α}, a ≤ b → bᶜ ≤ aᶜ- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- HeytingAlgebra
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.
- Compl.complstatement · cited by 2,925
- HeytingAlgebrastatement and proof · cited by 108
- compl_antiproof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- compl_iInfproof · cited by 6
- compl_le_compl_iff_leproof · cited by 5
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- Set.compl_subset_compl_of_subsetproof · cited by 2
- compl_le_of_compl_leproof · cited by 2
- Filter.totallyBounded_iff_filterproof · cited by 2
- Function.Embedding.schroeder_bernstein_of_relproof · cited by 2
- isCompact_closure_of_isTightMeasureSetproof · cited by 1
- Urysohns.CU.approx_mem_Icc_right_leftproof · cited by 1
- IsAntichain.monoproof · cited by 1
- Subalgebra.frontier_subset_frontierproof · cited by 1
- IsStrongAntichain.monoproof · cited by 0