Nuprl Lemma : unit-cube_wf
∀[I:Cname List]. (unit-cube(I) ∈ CubicalSet)
Proof
Definitions occuring in Statement :
unit-cube: unit-cube(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-set: CubicalSet,
unit-cube: unit-cube(I),
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
compose: f o g,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x]
Lemmas referenced :
name-morph_wf,
name-comp_wf,
subtype_rel_self,
name-comp-assoc,
name-comp-id-right,
compose_wf,
id-morph_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
because_Cache,
applyEquality,
sqequalRule,
universeIsType,
functionIsType,
lambdaFormation_alt,
functionExtensionality_alt,
equalitySymmetry,
independent_pairFormation,
productElimination,
productIsType,
equalityIstype,
baseClosed,
sqequalBase
Latex:
\mforall{}[I:Cname List]. (unit-cube(I) \mmember{} CubicalSet)
Date html generated:
2019_11_05-PM-00_25_55
Last ObjectModification:
2018_12_10-AM-09_43_12
Theory : cubical!sets
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