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Commit 2022-08-24 18:34 96ed4226

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feat(order/heyting_algebra): Heyting algebras (#15305) Define (generalized) Heyting, co-Heyting and bi-Heyting algebras. No lemma has been renamed, even though this might look like so from the diff. himp is now a field of boolean_algebra, with default value λ x y, y ⊔ xᶜ.

Duplicated lemmas

Those lemmas have been duplicated because they are true for Heyting algebras but are also used to prove that Boolean algebras are Heyting algebras:

  • sdiff_le'
  • inf_compl_eq_bot'

Changes to argument implicitness

  • sdiff_inf_self_left
  • sdiff_inf_self_right

Estimated changes

deleted theorem bot_sdiff
deleted theorem compl_bot
deleted theorem compl_inf_eq_bot
deleted theorem compl_le_compl
deleted theorem compl_sup
deleted theorem compl_top
deleted theorem disjoint_compl_left
deleted theorem disjoint_compl_right
added theorem himp_eq
added theorem hnot_eq_compl
added theorem inf_compl_eq_bot'
deleted theorem inf_compl_eq_bot
modified theorem inf_sdiff_right
modified theorem is_compl_compl
deleted theorem le_sdiff_sup
deleted theorem le_sup_sdiff
deleted theorem of_dual_compl
deleted theorem punit.bot_eq
deleted theorem punit.compl_eq
deleted theorem punit.inf_eq
deleted theorem punit.sdiff_eq
deleted theorem punit.sup_eq
deleted theorem punit.top_eq
deleted theorem sdiff_bot
modified theorem sdiff_compl
deleted theorem sdiff_eq_bot_iff
deleted theorem sdiff_inf
deleted theorem sdiff_inf_self_left
deleted theorem sdiff_inf_self_right
added theorem sdiff_le'
deleted theorem sdiff_le
deleted theorem sdiff_le_comm
deleted theorem sdiff_le_iff
deleted theorem sdiff_le_sdiff
deleted theorem sdiff_le_sdiff_left
deleted theorem sdiff_le_sdiff_right
deleted theorem sdiff_self
deleted theorem sdiff_top
modified theorem sup_sdiff_left
modified theorem sup_sdiff_right
deleted theorem to_dual_compl
modified theorem top_sdiff
added theorem bot_himp
added theorem bot_sdiff
added theorem codisjoint_hnot_left
added theorem codisjoint_hnot_right
added theorem compl_anti
added theorem compl_bot
added theorem compl_compl_compl
added theorem compl_iff_not
added theorem compl_inf_eq_bot
added theorem compl_inf_self
added theorem compl_le_compl
added theorem compl_le_himp
added theorem compl_le_hnot
added theorem compl_sup
added theorem compl_sup_compl_le
added theorem compl_sup_distrib
added theorem compl_sup_le_himp
added theorem compl_top
added theorem disjoint_compl_left
added theorem disjoint_compl_right
added theorem fst_compl
added theorem fst_himp
added theorem fst_hnot
added theorem fst_sdiff
added theorem himp_bot
added theorem himp_compl
added theorem himp_compl_comm
added theorem himp_eq_top_iff
added theorem himp_himp
added theorem himp_iff_imp
added theorem himp_inf_distrib
added theorem himp_inf_le
added theorem himp_inf_self
added theorem himp_le_himp
added theorem himp_le_himp_himp
added theorem himp_le_himp_left
added theorem himp_le_himp_right
added theorem himp_left_comm
added theorem himp_self
added theorem himp_top
added theorem hnot_anti
added theorem hnot_bot
added theorem hnot_hnot_hnot
added theorem hnot_hnot_le
added theorem hnot_hnot_sup_distrib
added theorem hnot_inf_distrib
added theorem hnot_le_comm
added theorem hnot_le_hnot
added theorem hnot_sdiff
added theorem hnot_sdiff_comm
added theorem hnot_sup_self
added theorem hnot_top
added theorem inf_compl_eq_bot
added theorem inf_compl_self
added theorem inf_himp
added theorem inf_himp_le
added theorem le_compl_comm
added theorem le_compl_compl
added theorem le_himp
added theorem le_himp_comm
added theorem le_himp_iff
added theorem le_himp_iff_left
added theorem le_hnot_inf_hnot
added theorem le_sdiff_sup
added theorem le_sup_sdiff
added theorem of_dual_compl
added theorem of_dual_himp
added theorem of_dual_hnot
added theorem pi.himp_apply
added theorem pi.himp_def
added theorem pi.hnot_apply
added theorem pi.hnot_def
added theorem punit.bot_eq
added theorem punit.compl_eq
added theorem punit.himp_eq
added theorem punit.hnot_eq
added theorem punit.inf_eq
added theorem punit.sdiff_eq
added theorem punit.sup_eq
added theorem punit.top_eq
added theorem sdiff_bot
added theorem sdiff_eq_bot_iff
added theorem sdiff_inf
added theorem sdiff_inf_distrib
added theorem sdiff_inf_self_left
added theorem sdiff_inf_self_right
added theorem sdiff_le
added theorem sdiff_le_comm
added theorem sdiff_le_hnot
added theorem sdiff_le_iff
added theorem sdiff_le_iff_left
added theorem sdiff_le_inf_hnot
added theorem sdiff_le_sdiff
added theorem sdiff_le_sdiff_left
added theorem sdiff_le_sdiff_right
added theorem sdiff_right_comm
added theorem sdiff_sdiff
added theorem sdiff_sdiff_le_sdiff
added theorem sdiff_self
added theorem sdiff_sup_self
added theorem sdiff_top
added theorem snd_compl
added theorem snd_himp
added theorem snd_hnot
added theorem snd_sdiff
added theorem sup_compl_le_himp
added theorem sup_himp_distrib
added theorem sup_himp_self_left
added theorem sup_himp_self_right
added theorem sup_hnot_self
added theorem sup_sdiff_distrib
added theorem sup_sdiff_self
added theorem to_dual_compl
added theorem to_dual_hnot
added theorem to_dual_sdiff
added theorem top_himp
added theorem top_sdiff'