Nuprl Lemma : forget-lattice_wf
ForgetLattice ∈ Functor(BddDistributiveLattice;TypeCat)
Proof
Definitions occuring in Statement :
forget-lattice: ForgetLattice,
distributive-lattice-cat: BddDistributiveLattice,
type-cat: TypeCat,
cat-functor: Functor(C1;C2),
member: t ∈ T
Definitions unfolded in proof :
forget-lattice: ForgetLattice,
member: t ∈ T,
distributive-lattice-cat: BddDistributiveLattice,
mk-cat: mk-cat,
all: ∀x:A. B[x],
top: Top,
type-cat: TypeCat,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3]
Lemmas referenced :
distributive-lattice-cat_wf,
type-cat_wf,
cat_ob_pair_lemma,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
cat-ob_wf,
cat_arrow_triple_lemma,
cat-arrow_wf,
cat_comp_tuple_lemma,
compose_wf,
bounded-lattice-hom_wf,
bdd-distributive-lattice_wf,
cat_id_tuple_lemma,
mk-functor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
because_Cache,
cumulativity,
universeEquality,
independent_isectElimination,
setElimination,
rename,
lambdaFormation
Latex:
ForgetLattice \mmember{} Functor(BddDistributiveLattice;TypeCat)
Date html generated:
2020_05_20-AM-09_00_30
Last ObjectModification:
2020_01_16-PM-05_05_39
Theory : lattices
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