Nuprl Lemma : csm-ap-restriction
∀X,Y:j⊢. ∀s:X j⟶ Y. ∀I,J:fset(ℕ). ∀f:J ⟶ I. ∀a:X(I). (f((s)a) = (s)f(a) ∈ Y(J))
Proof
Definitions occuring in Statement :
csm-ap: (s)x,
cube_set_map: A ⟶ B,
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
cube-cat: CubeCat,
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s),
csm-ap: (s)x,
pscm-ap: (s)x
Lemmas referenced :
pscm-ap-restriction,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}X,Y:j\mvdash{}. \mforall{}s:X j{}\mrightarrow{} Y. \mforall{}I,J:fset(\mBbbN{}). \mforall{}f:J {}\mrightarrow{} I. \mforall{}a:X(I). (f((s)a) = (s)f(a))
Date html generated:
2020_05_20-PM-01_42_52
Last ObjectModification:
2020_04_03-PM-03_34_40
Theory : cubical!type!theory
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