diff --git a/source/fundamentals/universes.mmt b/source/fundamentals/universes.mmt index cb75c180cc37193107b122ac43ef7b5d9a6747c4..cc997b4c49717154503389074724c32f26f6f5ea 100644 --- a/source/fundamentals/universes.mmt +++ b/source/fundamentals/universes.mmt @@ -54,3 +54,5 @@ theory UniverseDepFunExample = function_types: Pi_legal utp utpâ™ dependent_types: Pi_legal utp ukdâ™ âš + +// TODO these universes should be realized by corresponding theories of set-theoretical universeâš diff --git a/source/set_theory/axioms.mmt b/source/set_theory/axioms.mmt index f2c35d2bbeb9941f60c35a99037bf65cc010da19..4c631b972372549792ef66070796bc9b01da08c7 100644 --- a/source/set_theory/axioms.mmt +++ b/source/set_theory/axioms.mmt @@ -77,7 +77,7 @@ theory ReplacementAx = include ?RelationDefinitionsâ™ // The resulting set is a replacement for A regarding function fâ™ - isreplacement = [f,A,Z] ∀ͧ[y] y∈Z ⇔ (∃ͧ[x] x∈A ∧ f x y)â™ + isreplacement = [f,A,Z] ∀ͧ[y] y∈Z ⇔ (∃ͧ[x] x∈A ∧ f x y)â™ replacement_axiom : {f} ⊦ ∀ͧ[A] isfunction f A ⇒ ∃ͧ[Z] isreplacement f A Zâ™ replacement_unique : {f,A} ⊦ isfunction f A ⟶ ⊦ ∃êœÍ§[Z] isreplacement f A Z☠diff --git a/source/type_theory/endofunctors/collection_types.mmt b/source/type_theory/endofunctors/collection_types.mmt index 8ffd308fc3ecb21f67d7445c90435062b827cc15..1b3574987063d4708685607baff2b2214fe32650 100644 --- a/source/type_theory/endofunctors/collection_types.mmt +++ b/source/type_theory/endofunctors/collection_types.mmt @@ -116,7 +116,7 @@ theory MultisetSpec = include ?ListSpecâ™ include ?EndoCommutativeâ™ - intersect: {a} tm &a ⟶ tm &a ⟶ tm &aâ˜# %n 2 3 prec 30â™ + intersect: {a} tm &a ⟶ tm &a ⟶ tm &aâ˜# %n 2 3 prec 30â™ intersect_neutral1 : {a, xs: tm &a} ⊦ intersect neutral xs =Í neutralâ™ intersect_neutral2 : {a, xs: tm &a} ⊦ intersect xs neutral =Í neutralâ™ intersect_cons1: {a,x: tm a, xs,ys: tm &a}