Nuprl Lemma : cubical-subset-I_cube
∀[I,psi,J:Top]. (I,psi(J) ~ {f:J ⟶ I| (psi f) = 1} )
Proof
Definitions occuring in Statement :
cubical-subset: I,psi,
name-morph-satisfies: (psi f) = 1,
I_cube: A(I),
names-hom: I ⟶ J,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-subset: I,psi,
I_cube: A(I),
cube-cat: CubeCat,
rep-sub-sheaf: rep-sub-sheaf(C;X;P),
functor-ob: ob(F),
pi1: fst(t),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
cat_arrow_triple_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[I,psi,J:Top]. (I,psi(J) \msim{} \{f:J {}\mrightarrow{} I| (psi f) = 1\} )
Date html generated:
2018_05_23-AM-08_40_56
Last ObjectModification:
2018_05_20-PM-05_51_05
Theory : cubical!type!theory
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