Nuprl Lemma : universe-comp-fun_wf
∀[X:j⊢]. ∀[t:{X ⊢ _:c𝕌}]. (CompFun(t) ∈ X +⊢ Compositon(decode(t)))
Proof
Definitions occuring in Statement :
universe-comp-fun: CompFun(A),
universe-decode: decode(t),
cubical-universe: c𝕌,
composition-structure: Gamma ⊢ Compositon(A),
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe-comp-fun: CompFun(A),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
comp-op-to-comp-fun_wf2,
cubical_set_cumulativity-i-j,
universe-decode_wf,
universe-comp-op_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalRule,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
dependent_functionElimination,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[t:\{X \mvdash{} \_:c\mBbbU{}\}]. (CompFun(t) \mmember{} X +\mvdash{} Compositon(decode(t)))
Date html generated:
2020_05_20-PM-07_17_50
Last ObjectModification:
2020_04_27-PM-01_34_09
Theory : cubical!type!theory
Home
Index