Nuprl Lemma : rev-type-comp_wf
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 ⊢ Compositon(A)]. (rev-type-comp(Gamma;cA) ∈ Gamma.𝕀 ⊢ Compositon((A)-))
Proof
Definitions occuring in Statement :
rev-type-comp: rev-type-comp(Gamma;cA),
composition-structure: Gamma ⊢ Compositon(A),
rev-type-line: (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,
cc-snd: q,
interval-type: 𝕀,
cc-fst: p,
csm-ap-type: (AF)s,
constant-cubical-type: (X),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
rev-type-comp: rev-type-comp(Gamma;cA),
rev-type-line: (A)-
Lemmas referenced :
interval-rev_wf,
cube-context-adjoin_wf,
interval-type_wf,
cc-snd_wf,
subset-cubical-term2,
sub_cubical_set_self,
csm-ap-type_wf,
cc-fst_wf,
csm-interval-type,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf,
csm-adjoin_wf,
csm-comp-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
hypothesis,
hypothesisEquality,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
independent_isectElimination,
Error :memTop,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. \mforall{}[cA:Gamma.\mBbbI{} \mvdash{} Compositon(A)].
(rev-type-comp(Gamma;cA) \mmember{} Gamma.\mBbbI{} \mvdash{} Compositon((A)-))
Date html generated:
2020_05_20-PM-04_36_49
Last ObjectModification:
2020_04_13-PM-00_43_29
Theory : cubical!type!theory
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