Nuprl Lemma : contractible_comp_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[cA:X +⊢ Compositon(A)]. (contractible_comp(X;A;cA) ∈ X ⊢ Compositon(Contractible(A)))
Proof
Definitions occuring in Statement :
contractible_comp: contractible_comp(X;A;cA),
composition-structure: Gamma ⊢ Compositon(A),
contractible-type: Contractible(A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
contractible-type: Contractible(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
contractible_comp: contractible_comp(X;A;cA),
subtype_rel: A ⊆r B
Lemmas referenced :
sigma_comp_wf2,
cubical-pi_wf,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-ap-type_wf,
cc-fst_wf,
path-type_wf,
csm-ap-term_wf,
cc-snd_wf,
composition-structure-cumulativity,
pi_comp_wf2,
csm-comp-structure_wf,
path_comp_wf,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
because_Cache,
hypothesis,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[cA:X +\mvdash{} Compositon(A)].
(contractible\_comp(X;A;cA) \mmember{} X \mvdash{} Compositon(Contractible(A)))
Date html generated:
2020_05_20-PM-05_14_03
Last ObjectModification:
2020_04_17-AM-00_16_02
Theory : cubical!type!theory
Home
Index