Nuprl Lemma : pscm-ap-comp-type-sq2
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[s1,s2:Top]. (((A)s2)s1 ~ (A)s2 o s1)
Proof
Definitions occuring in Statement :
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
pscm-comp: G o F,
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,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-top,
presheaf-type_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf,
pscm-ap-comp-type-sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
axiomSqEquality,
because_Cache,
cut,
extract_by_obid,
hypothesis,
universeIsType,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
sqequalRule,
Error :memTop
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[s1,s2:Top].
(((A)s2)s1 \msim{} (A)s2 o s1)
Date html generated:
2020_05_20-PM-01_26_29
Last ObjectModification:
2020_04_01-AM-11_00_57
Theory : presheaf!models!of!type!theory
Home
Index