Nuprl Lemma : free-dist-lattice-adjunction
FreeDistLattice -| ForgetLattice
Proof
Definitions occuring in Statement :
forget-lattice: ForgetLattice,
free-dl-functor: FreeDistLattice,
distributive-lattice-cat: BddDistributiveLattice,
counit-unit-adjunction: F -| G,
type-cat: TypeCat
Definitions unfolded in proof :
all: ∀x:A. B[x],
lattice-point: Point(l),
record-select: r.x,
free-dl: free-dl(X),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
free-dl-type: free-dl-type(X),
quotient: x,y:A//B[x; y],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
free-dl-functor: FreeDistLattice,
distributive-lattice-cat: BddDistributiveLattice,
top: Top,
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
so_apply: x[s],
forget-lattice: ForgetLattice,
mk-cat: mk-cat,
bdd-distributive-lattice: BoundedDistributiveLattice,
cat-ob: cat-ob(C),
pi1: fst(t),
type-cat: TypeCat,
guard: {T},
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
and: P ∧ Q,
counit-unit-equations: counit-unit-equations(D;C;F;G;eps;eta),
cand: A c∧ B,
compose: f o g,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
squash: ↓T,
true: True,
free-dl-generator: free-dl-generator(x),
fdl-hom: fdl-hom(L;f),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cons: [a / b]
Lemmas referenced :
free-dl-generator_wf,
mk-adjunction_wf,
type-cat_wf,
distributive-lattice-cat_wf,
free-dl-functor_wf,
forget-lattice_wf,
ob_mk_functor_lemma,
cat_arrow_triple_lemma,
fdl-hom_wf,
lattice-point_wf,
cat-ob_wf,
arrow_mk_functor_lemma,
cat_ob_pair_lemma,
cat_comp_tuple_lemma,
bounded-lattice-hom_wf,
bdd-distributive-lattice_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_id_tuple_lemma,
free-dl-generators,
free-dl_wf,
id-is-bounded-lattice-hom,
bdd-distributive-lattice-subtype-bdd-lattice,
subtype_rel_self,
compose-bounded-lattice-hom,
fdl-hom-agrees,
squash_wf,
true_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
lattice-0_wf,
lattice-1-meet,
iff_weakening_equal,
lattice-join-0
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
universeEquality,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
because_Cache,
instantiate,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
functionEquality,
productEquality,
cumulativity,
independent_pairFormation,
applyLambdaEquality,
hyp_replacement,
equalitySymmetry,
imageElimination,
equalityTransitivity,
natural_numberEquality,
imageMemberEquality,
baseClosed,
functionExtensionality,
productElimination,
independent_functionElimination,
comment
Latex:
FreeDistLattice -| ForgetLattice
Date html generated:
2020_05_20-AM-09_00_39
Last ObjectModification:
2020_01_16-PM-05_06_39
Theory : lattices
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