Nuprl Lemma : univ-comp_wf
∀[G:j⊢]. (univ-comp{i:l}() ∈ G ⊢ CompOp(c𝕌))
Proof
Definitions occuring in Statement :
univ-comp: univ-comp{i:l}(),
cubical-universe: c𝕌,
composition-op: Gamma ⊢ CompOp(A),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
univ-comp-sq,
comp-fun-to-comp-op_wf,
cubical-universe_wf,
compU_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
hypothesis,
instantiate,
dependent_functionElimination,
hypothesisEquality,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. (univ-comp\{i:l\}() \mmember{} G \mvdash{} CompOp(c\mBbbU{}))
Date html generated:
2020_05_20-PM-07_23_48
Last ObjectModification:
2020_04_28-PM-00_12_38
Theory : cubical!type!theory
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