Nuprl Lemma : typed-psc-snd_wf
∀C:SmallCategory. ∀G:ps_context{j:l}(C). ∀A:{G ⊢ _}. (tq ∈ {G.A ⊢ _:(A)tp{i:l}})
Proof
Definitions occuring in Statement :
typed-psc-snd: tq,
typed-psc-fst: tp{i:l},
psc-adjoin: X.A,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
all: ∀x:A. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
all: ∀x:A. B[x],
typed-psc-fst: tp{i:l},
typed-psc-snd: tq,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
psc-snd_wf,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
applyEquality
Latex:
\mforall{}C:SmallCategory. \mforall{}G:ps\_context\{j:l\}(C). \mforall{}A:\{G \mvdash{} \_\}. (tq \mmember{} \{G.A \mvdash{} \_:(A)tp\{i:l\}\})
Date html generated:
2020_05_20-PM-01_27_37
Last ObjectModification:
2020_04_02-PM-00_30_11
Theory : presheaf!models!of!type!theory
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