Nuprl Lemma : const-transport-fun_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[cA:Gamma ⊢ CompOp(A)]. (ConstTrans(A) ∈ {Gamma ⊢ _:(A ⟶ A)})
Proof
Definitions occuring in Statement :
const-transport-fun: ConstTrans(A),
composition-op: Gamma ⊢ CompOp(A),
cubical-fun: (A ⟶ B),
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,
const-transport-fun: ConstTrans(A),
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-lam_wf,
transport-const_wf,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-ap-type_wf,
cc-fst_wf,
csm-composition_wf,
cc-snd_wf,
composition-op_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
because_Cache,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[cA:Gamma \mvdash{} CompOp(A)]. (ConstTrans(A) \mmember{} \{Gamma \mvdash{} \_:(A {}\mrightarrow{} A)\})
Date html generated:
2020_05_20-PM-04_18_58
Last ObjectModification:
2020_04_10-AM-04_54_45
Theory : cubical!type!theory
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