Nuprl Lemma : pscm-ap-term-snd-adjoin
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. ∀[xx:Top]. ((q)(xx;u) = u ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
pscm-adjoin: (s;u),
psc-snd: q,
pscm-ap-term: (t)s,
presheaf-term: {X ⊢ _:A},
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pscm-ap-term: (t)s,
pscm-adjoin: (s;u),
pscm-ap: (s)x,
psc-snd: q,
pi2: snd(t),
subtype_rel: A ⊆r B,
presheaf-term: {X ⊢ _:A},
uimplies: b supposing a
Lemmas referenced :
istype-top,
presheaf-term_wf,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf,
presheaf-term-equal,
I_set_wf,
cat-ob_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality_alt,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate,
applyEquality,
equalitySymmetry,
lambdaEquality_alt,
setElimination,
rename,
independent_isectElimination,
functionExtensionality_alt
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. \mforall{}[xx:Top].
((q)(xx;u) = u)
Date html generated:
2020_05_20-PM-01_28_28
Last ObjectModification:
2020_04_02-PM-01_56_11
Theory : presheaf!models!of!type!theory
Home
Index