Nuprl Lemma : rev-transport-fun_wf
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 ⊢ CompOp(A)].
(rev-transport-fun(Gamma;A;cA) ∈ {Gamma ⊢ _:((A)[1(𝕀)] ⟶ (A)[0(𝕀)])})
Proof
Definitions occuring in Statement :
rev-transport-fun: rev-transport-fun(Gamma;A;cA),
composition-op: Gamma ⊢ CompOp(A),
interval-1: 1(𝕀),
interval-0: 0(𝕀),
interval-type: 𝕀,
cubical-fun: (A ⟶ B),
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
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,
subtype_rel: A ⊆r B,
cc-snd: q,
interval-type: 𝕀,
cc-fst: p,
csm-ap-type: (AF)s,
constant-cubical-type: (X),
rev-type-line: (A)-,
rev-transport-fun: rev-transport-fun(Gamma;A;cA)
Lemmas referenced :
csm-adjoin_wf,
cubical_set_cumulativity-i-j,
cube-context-adjoin_wf,
interval-type_wf,
cc-fst_wf,
csm-interval-type,
interval-rev_wf,
cc-snd_wf,
csm-composition_wf,
transport-fun_wf,
rev-type-line_wf,
composition-op_wf,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf,
rev-type-line-0,
rev-type-line-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. \mforall{}[cA:Gamma.\mBbbI{} \mvdash{} CompOp(A)].
(rev-transport-fun(Gamma;A;cA) \mmember{} \{Gamma \mvdash{} \_:((A)[1(\mBbbI{})] {}\mrightarrow{} (A)[0(\mBbbI{})])\})
Date html generated:
2020_05_20-PM-04_19_12
Last ObjectModification:
2020_04_10-AM-04_55_14
Theory : cubical!type!theory
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