Nuprl Lemma : pscm-ap-id-term
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}].
((t)1(Gamma) = t ∈ {Gamma ⊢ _:A})
Proof
Definitions occuring in Statement :
pscm-ap-term: (t)s,
presheaf-term: {X ⊢ _:A},
presheaf-type: {X ⊢ _},
pscm-id: 1(X),
ps_context: __⊢,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-term: {X ⊢ _:A},
subtype_rel: A ⊆r B,
pscm-id: 1(X),
pscm-ap-term: (t)s,
pscm-ap: (s)x,
all: ∀x:A. B[x]
Lemmas referenced :
presheaf-term_wf,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf,
I_set_wf,
cat-ob_wf,
cat-arrow_wf,
presheaf-type-at_wf,
psc-restriction_wf,
presheaf-type-ap-morph_wf,
ps_context_cumulativity2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
equalitySymmetry,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
hypothesis,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
applyEquality,
functionExtensionality_alt,
functionIsType,
because_Cache,
equalityIstype
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}].
((t)1(Gamma) = t)
Date html generated:
2020_05_20-PM-01_26_58
Last ObjectModification:
2020_04_01-PM-01_51_07
Theory : presheaf!models!of!type!theory
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