Nuprl Lemma : csm-ap-comp-term
∀[Gamma,Delta,Z:j⊢]. ∀[s1:Z j⟶ Delta]. ∀[s2:Delta j⟶ Gamma]. ∀[A:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}].
((t)s2 o s1 = ((t)s2)s1 ∈ {Z ⊢ _:(A)s2 o s1})
Proof
Definitions occuring in Statement :
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
csm-comp: G o F,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
csm-comp: G o F,
pscm-comp: G o F,
csm-ap-term: (t)s,
pscm-ap-term: (t)s
Lemmas referenced :
pscm-ap-comp-term,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[Gamma,Delta,Z:j\mvdash{}]. \mforall{}[s1:Z j{}\mrightarrow{} Delta]. \mforall{}[s2:Delta j{}\mrightarrow{} Gamma]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}].
((t)s2 o s1 = ((t)s2)s1)
Date html generated:
2020_05_20-PM-01_53_51
Last ObjectModification:
2020_04_03-PM-08_28_36
Theory : cubical!type!theory
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