Nuprl Lemma : cubical-universe_wf
c𝕌 ∈ CubicalSet'
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
cubical-set: CubicalSet,
member: t ∈ T
Definitions unfolded in proof :
cubical-universe: c𝕌,
member: t ∈ T,
cubical-set: CubicalSet,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
cand: A c∧ B,
compose: f o g
Lemmas referenced :
all_wf,
list_wf,
coordinate_name_wf,
name-morph_wf,
equal_wf,
name-comp_wf,
compose_wf,
equal-wf-T-base,
id-morph_wf,
Kan-cubical-type_wf,
unit-cube_wf,
csm-Kan-cubical-type_wf,
unit-cube-map_wf,
csm-Kan-unit-cube-comp,
csm-Kan-unit-cube-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
sqequalRule,
spreadEquality,
hypothesisEquality,
productEquality,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
baseClosed,
dependent_pairEquality,
functionExtensionality,
lambdaFormation,
dependent_functionElimination,
independent_pairFormation
Latex:
c\mBbbU{} \mmember{} CubicalSet'
Date html generated:
2018_05_23-PM-07_28_22
Last ObjectModification:
2018_05_20-PM-05_29_11
Theory : cubical!sets
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