Nuprl Lemma : rev-type-line-comp_wf
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 ⊢ CompOp(A)]. ((cA)- ∈ Gamma.𝕀 ⊢ CompOp((A)-))
Proof
Definitions occuring in Statement :
rev-type-line-comp: (cA)-,
rev-type-line: (A)-,
composition-op: Gamma ⊢ CompOp(A),
interval-type: 𝕀,
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rev-type-line-comp: (cA)-,
rev-type-line: (A)-,
subtype_rel: A ⊆r B,
cc-snd: q,
interval-type: 𝕀,
cc-fst: p,
csm-ap-type: (AF)s,
constant-cubical-type: (X)
Lemmas referenced :
csm-composition_wf,
cube-context-adjoin_wf,
interval-type_wf,
csm-adjoin_wf,
cc-fst_wf,
csm-interval-type,
interval-rev_wf,
cc-snd_wf,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. \mforall{}[cA:Gamma.\mBbbI{} \mvdash{} CompOp(A)]. ((cA)- \mmember{} Gamma.\mBbbI{} \mvdash{} CompOp((A)-))
Date html generated:
2020_05_20-PM-04_17_47
Last ObjectModification:
2020_04_10-AM-04_51_45
Theory : cubical!type!theory
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