Nuprl Lemma : composition-op_wf1
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢j _}]. (Gamma ⊢ CompOp(A) ∈ 𝕌{[i | j]'})
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
composition-op: Gamma ⊢ CompOp(A),
comp-op: comp-op(Gamma;A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
comp-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
composition-uniformity_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
setEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{}j \_\}]. (Gamma \mvdash{} CompOp(A) \mmember{} \mBbbU{}\{[i | j]'\})
Date html generated:
2020_05_20-PM-03_49_19
Last ObjectModification:
2020_04_09-PM-01_10_36
Theory : cubical!type!theory
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