Nuprl Lemma : csm-ap_wf
∀[X,Y:j⊢]. ∀[s:X j⟶ Y]. ∀[I:fset(ℕ)]. ∀[x:X(I)]. ((s)x ∈ Y(I))
Proof
Definitions occuring in Statement :
csm-ap: (s)x,
cube_set_map: A ⟶ B,
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
csm-ap: (s)x,
pscm-ap: (s)x
Lemmas referenced :
pscm-ap_wf,
cube-cat_wf,
cat_ob_pair_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[X,Y:j\mvdash{}]. \mforall{}[s:X j{}\mrightarrow{} Y]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:X(I)]. ((s)x \mmember{} Y(I))
Date html generated:
2020_05_20-PM-01_41_26
Last ObjectModification:
2020_04_03-PM-03_33_46
Theory : cubical!type!theory
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