Nuprl Lemma : cubes-comp
∀[X:Top]. (cat-comp(cubes(X)) ~ λAa,Bb,_,f,g. g ⋅ f)
Proof
Definitions occuring in Statement :
cubes: cubes(X),
nh-comp: g ⋅ f,
cat-comp: cat-comp(C),
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubes: cubes(X),
cube-cat: CubeCat,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
sets-comp,
cube-cat_wf,
cat_comp_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[X:Top]. (cat-comp(cubes(X)) \msim{} \mlambda{}Aa,Bb,$_{}$,f,g. g \mcdot{} f)
Date html generated:
2018_05_23-AM-08_33_29
Last ObjectModification:
2018_05_20-PM-05_46_31
Theory : cubical!type!theory
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