Nuprl Lemma : revfill-1
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 ⊢ Compositon(A)]. ∀[a1:{Gamma ⊢ _:(A)[1(𝕀)]}].
((revfill(Gamma;cA;a1))[1(𝕀)] = a1 ∈ {Gamma ⊢ _:(A)[1(𝕀)]})
Proof
Definitions occuring in Statement :
revfill: revfill(Gamma;cA;a1),
composition-structure: Gamma ⊢ Compositon(A),
interval-1: 1(𝕀),
interval-type: 𝕀,
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
revfill: revfill(Gamma;cA;a1),
member: t ∈ T,
subtype_rel: A ⊆r B,
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]},
uimplies: b supposing a
Lemmas referenced :
cubical-term_wf,
csm-ap-type_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
csm-id-adjoin_wf-interval-1,
cubical-type-cumulativity2,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf,
rev_fill_term_1,
face-0_wf,
csm-face-0,
empty-context-subset-lemma3,
subset-cubical-term,
context-subset_wf,
context-subset-is-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
hypothesis,
universeIsType,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
because_Cache,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality_alt,
equalityIstype,
inhabitedIsType,
independent_isectElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. \mforall{}[cA:Gamma.\mBbbI{} \mvdash{} Compositon(A)]. \mforall{}[a1:\{Gamma \mvdash{} \_:(A)[1(\mBbbI{})]\}].
((revfill(Gamma;cA;a1))[1(\mBbbI{})] = a1)
Date html generated:
2020_05_20-PM-04_53_19
Last ObjectModification:
2020_04_14-AM-11_56_58
Theory : cubical!type!theory
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