Nuprl Lemma : cubical-interval_wf
cubical-interval() ∈ CubicalSet
Proof
Definitions occuring in Statement :
cubical-interval: cubical-interval(),
cubical-set: CubicalSet,
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
cubical-set: CubicalSet,
cubical-interval: cubical-interval(),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
compose: f o g,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morph_wf,
nil_wf,
coordinate_name_wf,
int_seg_wf,
list_wf,
name-comp_wf,
equal_wf,
squash_wf,
true_wf,
name-comp-assoc,
iff_weakening_equal,
name-comp-id-left,
all_wf,
compose_wf,
equal-wf-T-base,
id-morph_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
dependent_pairEquality,
lambdaEquality,
functionEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
sqequalRule,
applyEquality,
because_Cache,
functionExtensionality,
lambdaFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
productEquality
Latex:
cubical-interval() \mmember{} CubicalSet
Date html generated:
2017_10_05-AM-10_12_22
Last ObjectModification:
2017_07_28-AM-11_18_14
Theory : cubical!sets
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