Nuprl Lemma : pscm-comp-sq
∀[C:SmallCategory]. ∀[A,B,E,F,G:Top]. (G o F ~ F o G)
Proof
Definitions occuring in Statement :
pscm-comp: G o F,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t,
type-cat: TypeCat,
op-cat: op-cat(C),
trans-comp: t1 o t2,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-cat: TypeCat,
trans-comp: t1 o t2,
pscm-comp: G o F,
all: ∀x:A. B[x],
mk-nat-trans: x |→ T[x]
Lemmas referenced :
cat_comp_tuple_lemma,
istype-top,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
axiomSqEquality,
inhabitedIsType,
hypothesisEquality,
isect_memberEquality_alt,
isectElimination,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A,B,E,F,G:Top]. (G o F \msim{} F o G)
Date html generated:
2020_05_20-PM-01_24_05
Last ObjectModification:
2020_04_01-AM-09_40_19
Theory : presheaf!models!of!type!theory
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