Nuprl Lemma : pscm-ap-type-fst-adjoin
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[B:{X ⊢ _}]. ∀[s,u:Top]. (((B)p)(s;u) ~ (B)s)
Proof
Definitions occuring in Statement :
pscm-adjoin: (s;u),
psc-fst: p,
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-type: {X ⊢ _},
pscm-ap-type: (AF)s,
psc-fst: p,
pscm-adjoin: (s;u),
pscm-ap: (s)x,
pi1: fst(t),
subtype_rel: A ⊆r B
Lemmas referenced :
istype-top,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
sqequalRule,
axiomSqEquality,
hypothesis,
because_Cache,
extract_by_obid,
universeIsType,
isectElimination,
hypothesisEquality,
instantiate,
applyEquality
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[B:\{X \mvdash{} \_\}]. \mforall{}[s,u:Top]. (((B)p)(s;u) \msim{} (B)s)
Date html generated:
2020_05_20-PM-01_28_19
Last ObjectModification:
2020_04_02-PM-01_56_06
Theory : presheaf!models!of!type!theory
Home
Index