Nuprl Lemma : psc-fstfst_wf
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[B:{Gamma.A ⊢ _}].
(pp ∈ psc_map{[i | j]:l}(C; Gamma.A.B; Gamma))
Proof
Definitions occuring in Statement :
psc-fstfst: pp,
psc-adjoin: X.A,
presheaf-type: {X ⊢ _},
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
psc-fstfst: pp,
subtype_rel: A ⊆r B,
psc-adjoin: X.A,
all: ∀x:A. B[x],
pi1: fst(t),
psc-restriction: f(s),
pi2: snd(t)
Lemmas referenced :
psc-map-is,
psc-adjoin_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
presheaf-type_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf,
pi1_wf_top,
I_set_wf,
top_wf,
I_set_pair_redex_lemma,
cat-ob_wf,
cat-arrow_wf,
psc_restriction_pair_lemma,
psc-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
dependent_set_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
lambdaEquality_alt,
productEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
Error :memTop,
productElimination,
independent_pairEquality,
lambdaFormation_alt,
functionIsType,
equalityIstype
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[B:\{Gamma.A \mvdash{} \_\}].
(pp \mmember{} psc\_map\{[i | j]:l\}(C; Gamma.A.B; Gamma))
Date html generated:
2020_05_20-PM-01_27_31
Last ObjectModification:
2020_04_03-AM-11_58_38
Theory : presheaf!models!of!type!theory
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