Nuprl Lemma : comp-op-to-comp-fun-univ-comp
∀[G:j⊢]. (cop-to-cfun(univ-comp{i:l}()) ∈ composition-structure{[i' | j]:l, i':l}(G; c𝕌))
Proof
Definitions occuring in Statement :
univ-comp: univ-comp{i:l}(),
cubical-universe: c𝕌,
comp-op-to-comp-fun: cop-to-cfun(cA),
composition-structure: Gamma ⊢ Compositon(A),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
comp-op-to-comp-fun_wf2,
cubical_set_cumulativity-i-j,
cubical-universe_wf,
univ-comp_wf,
univ-comp-sq,
comp-fun-to-comp-op_wf,
trivial-cube-set_wf,
compU_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
Error :memTop,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. (cop-to-cfun(univ-comp\{i:l\}()) \mmember{} composition-structure\{[i' | j]:l, i':l\}(G; c\mBbbU{}))
Date html generated:
2020_05_20-PM-07_24_03
Last ObjectModification:
2020_04_28-PM-01_02_07
Theory : cubical!type!theory
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