Nuprl Lemma : transprt-const_wf
∀[G:j⊢]. ∀[A:{G ⊢ _}]. ∀[cA:G +⊢ Compositon(A)]. ∀[a:{G ⊢ _:A}]. (transprt-const(G;cA;a) ∈ {G ⊢ _:A})
Proof
Definitions occuring in Statement :
transprt-const: transprt-const(G;cA;a),
composition-structure: Gamma ⊢ Compositon(A),
cubical-term: {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,
subtype_rel: A ⊆r B,
cubical-type: {X ⊢ _},
csm-id: 1(X),
csm-ap-type: (AF)s,
cc-fst: p,
interval-0: 0(𝕀),
csm-id-adjoin: [u],
csm-ap: (s)x,
csm-adjoin: (s;u),
pi1: fst(t),
interval-1: 1(𝕀),
uimplies: b supposing a,
transprt-const: transprt-const(G;cA;a),
squash: ↓T,
true: True
Lemmas referenced :
transprt_wf,
csm-ap-type_wf,
cube-context-adjoin_wf,
interval-type_wf,
cc-fst_wf,
csm-comp-structure_wf,
subset-cubical-term2,
sub_cubical_set_self,
csm-id_wf,
csm-ap-id-type,
istype-cubical-term,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf,
cubical-term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
setElimination,
rename,
productElimination,
independent_isectElimination,
equalitySymmetry,
axiomEquality,
equalityTransitivity,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
lambdaEquality_alt,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
hyp_replacement
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A:\{G \mvdash{} \_\}]. \mforall{}[cA:G +\mvdash{} Compositon(A)]. \mforall{}[a:\{G \mvdash{} \_:A\}].
(transprt-const(G;cA;a) \mmember{} \{G \mvdash{} \_:A\})
Date html generated:
2020_05_20-PM-04_39_03
Last ObjectModification:
2020_04_14-PM-10_28_55
Theory : cubical!type!theory
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