Nuprl Lemma : csm-comp-structure_wf2
∀[Gamma,Delta:j⊢]. ∀[tau:Delta j⟶ Gamma]. ∀[A:{Gamma ⊢ _}]. ∀[cA:Gamma +⊢ Compositon(A)].
((cA)tau ∈ Delta +⊢ Compositon((A)tau))
Proof
Definitions occuring in Statement :
csm-comp-structure: (cA)tau,
composition-structure: Gamma ⊢ Compositon(A),
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
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,
csm-comp-structure: (cA)tau,
interval-type: 𝕀,
csm-comp: G o F,
compose: f o g
Lemmas referenced :
csm-comp-structure_wf,
cubical_set_cumulativity-i-j,
cube_set_map_cumulativity-i-j,
composition-structure_wf,
cubical-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma,Delta:j\mvdash{}]. \mforall{}[tau:Delta j{}\mrightarrow{} Gamma]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[cA:Gamma +\mvdash{} Compositon(A)].
((cA)tau \mmember{} Delta +\mvdash{} Compositon((A)tau))
Date html generated:
2020_05_20-PM-04_35_36
Last ObjectModification:
2020_04_23-PM-01_10_44
Theory : cubical!type!theory
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