Nuprl Lemma : cube-cat-final
Final({})
Proof
Definitions occuring in Statement :
cube-cat: CubeCat,
cat-final: Final(fnl),
empty-fset: {}
Definitions unfolded in proof :
cube-cat: CubeCat,
cat-final: Final(fnl),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
names-hom: I ⟶ J,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
names: names(I),
false: False,
not: ¬A,
implies: P ⇒ Q,
fset-member: a ∈ s,
assert: ↑b,
ifthenelse: if b then t else f fi ,
deq-member: x ∈b L,
reduce: reduce(f;k;as),
list_ind: list_ind,
empty-fset: {},
nil: [],
it: ⋅,
bfalse: ff,
nat: ℕ
Lemmas referenced :
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
names_wf,
empty-fset_wf,
nat_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
functionEquality,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
axiomEquality,
independent_pairFormation,
lambdaFormation,
functionExtensionality,
setElimination,
rename,
independent_functionElimination,
intEquality,
natural_numberEquality
Latex:
Final(\{\})
Date html generated:
2018_05_23-AM-08_29_07
Last ObjectModification:
2018_05_20-PM-05_39_45
Theory : cubical!type!theory
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