Nuprl Lemma : cubical-subset-restriction
∀[I,J,K,f,g,phi:Top]. (g(f) ~ f ⋅ g)
Proof
Definitions occuring in Statement :
cubical-subset: I,psi,
cube-set-restriction: f(s),
nh-comp: g ⋅ f,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
cubical-subset: I,psi,
cube-set-restriction: f(s),
cube-cat: CubeCat,
rep-sub-sheaf: rep-sub-sheaf(C;X;P),
pi2: snd(t),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
cat_comp_tuple_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[I,J,K,f,g,phi:Top]. (g(f) \msim{} f \mcdot{} g)
Date html generated:
2018_05_23-AM-08_41_02
Last ObjectModification:
2018_05_20-PM-05_51_16
Theory : cubical!type!theory
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