Nuprl Lemma : cube-set-restriction-comp2
∀X:j⊢. ∀I,J1,J2,K:fset(ℕ). ∀f:J1 ⟶ I. ∀g:K ⟶ J1. ∀a:X(I). g(f(a)) = f ⋅ g(a) ∈ X(K) supposing J1 = J2 ∈ fset(ℕ)
Proof
Definitions occuring in Statement :
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
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-cat: CubeCat,
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
psc-restriction-comp2,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_comp_tuple_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:j\mvdash{}. \mforall{}I,J1,J2,K:fset(\mBbbN{}). \mforall{}f:J1 {}\mrightarrow{} I. \mforall{}g:K {}\mrightarrow{} J1. \mforall{}a:X(I). g(f(a)) = f \mcdot{} g(a) supposing J1 = J2
Date html generated:
2020_05_20-PM-01_42_40
Last ObjectModification:
2020_04_03-PM-03_34_32
Theory : cubical!type!theory
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