Nuprl Lemma : csm-equal2
∀[A,B:j⊢]. ∀[f,g:A j⟶ B]. f = g ∈ A j⟶ B supposing ∀K:fset(ℕ). ∀x:A(K). ((f K x) = (g K x) ∈ B(K))
Proof
Definitions occuring in Statement :
cube_set_map: A ⟶ B,
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
equal: s = 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)
Lemmas referenced :
pscm-equal2,
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{}[A,B:j\mvdash{}]. \mforall{}[f,g:A j{}\mrightarrow{} B]. f = g supposing \mforall{}K:fset(\mBbbN{}). \mforall{}x:A(K). ((f K x) = (g K x))
Date html generated:
2020_05_20-PM-01_41_14
Last ObjectModification:
2020_04_03-PM-03_33_38
Theory : cubical!type!theory
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