Nuprl Lemma : psc-m2_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}]. (q2 ∈ {X.A.B ⊢ _:((A)p)p})
Proof
Definitions occuring in Statement :
psc-m2: q2,
psc-fst: p,
psc-adjoin: X.A,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
psc-m2: q2,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
psc-snd_wf,
pscm-ap-type_wf,
ps_context_cumulativity2,
psc-adjoin_wf,
presheaf-type-cumulativity2,
psc-fst_wf,
pscm-ap-term_wf,
presheaf-term_wf,
presheaf-type_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
inhabitedIsType,
lambdaFormation_alt,
instantiate,
applyEquality,
because_Cache,
sqequalRule,
universeIsType,
equalityIstype,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[B:\{X.A \mvdash{} \_\}].
(q2 \mmember{} \{X.A.B \mvdash{} \_:((A)p)p\})
Date html generated:
2020_05_20-PM-01_27_39
Last ObjectModification:
2020_04_02-PM-01_36_12
Theory : presheaf!models!of!type!theory
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