Nuprl Lemma : csm-comp-structure-composition-function
∀[Gamma,Delta:j⊢]. ∀[tau:Delta j⟶ Gamma]. ∀[A:{Gamma ⊢ _}]. ∀[cA:Gamma ⊢ Compositon(A)].
((cA)tau ∈ composition-function{j:l,i:l}(Delta;(A)tau))
Proof
Definitions occuring in Statement :
csm-comp-structure: (cA)tau,
composition-structure: Gamma ⊢ Compositon(A),
composition-function: composition-function{j:l,i:l}(Gamma;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,
composition-structure: Gamma ⊢ Compositon(A)
Lemmas referenced :
csm-comp-structure_wf,
composition-structure_wf,
cubical-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
universeIsType,
inhabitedIsType,
instantiate,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
lambdaEquality_alt,
setElimination,
rename
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{} composition-function\{j:l,i:l\}(Delta;(A)tau))
Date html generated:
2020_05_20-PM-04_35_50
Last ObjectModification:
2020_04_13-PM-00_43_14
Theory : cubical!type!theory
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