Nuprl Lemma : presheaf-it-unique
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[t:{X ⊢ _:1}]. (t = * ∈ {X ⊢ _:1})
Proof
Definitions occuring in Statement :
presheaf-it: *,
presheaf-unit: 1,
presheaf-term: {X ⊢ _:A},
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-unit: 1,
discrete-presheaf-type: discr(T),
all: ∀x:A. B[x],
presheaf-term-at: u(a),
subtype_rel: A ⊆r B,
presheaf-type-at: A(a),
pi1: fst(t),
unit: Unit,
uimplies: b supposing a
Lemmas referenced :
presheaf_type_at_pair_lemma,
equal-unit,
presheaf-term-at_wf,
presheaf-unit_wf,
subtype_rel_self,
unit_wf2,
presheaf-it_wf,
small-category-cumulativity-2,
ps_context_cumulativity2,
I_set_wf,
cat-ob_wf,
presheaf-term-equal,
presheaf-term_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
functionExtensionality,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[t:\{X \mvdash{} \_:1\}]. (t = *)
Date html generated:
2020_05_20-PM-01_34_48
Last ObjectModification:
2020_04_02-PM-06_34_13
Theory : presheaf!models!of!type!theory
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