Nuprl Lemma : csm-swap_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _}]. (csm-swap(G;A;B) ∈ G.A.(B)p ij⟶ G.B.(A)p)
Proof
Definitions occuring in Statement :
csm-swap: csm-swap(G;A;B),
cc-fst: p,
cube-context-adjoin: X.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,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
cube-context-adjoin: X.A,
psc-adjoin: X.A,
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f),
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
cc-fst: p,
psc-fst: p,
csm-swap: csm-swap(G;A;B),
pscm-swap: pscm-swap(G;A;B),
csm-adjoin: (s;u),
pscm-adjoin: (s;u),
csm+: tau+,
pscm+: tau+,
csm-comp: G o F,
pscm-comp: G o F,
cc-snd: q,
psc-snd: q,
csm-ap-term: (t)s,
pscm-ap-term: (t)s
Lemmas referenced :
pscm-swap_wf,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_\}]. (csm-swap(G;A;B) \mmember{} G.A.(B)p ij{}\mrightarrow{} G.B.(A)p)
Date html generated:
2020_05_20-PM-01_58_58
Last ObjectModification:
2020_04_04-AM-09_39_53
Theory : cubical!type!theory
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