Nuprl Lemma : cubical-term-equal
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. ∀[z:I:fset(ℕ) ⟶ a:X(I) ⟶ A(a)].
u = z ∈ {X ⊢ _:A} supposing u = z ∈ (I:fset(ℕ) ⟶ a:X(I) ⟶ A(a))
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a)
Lemmas referenced :
presheaf-term-equal,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term,
cat_ob_pair_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop,
dependent_functionElimination
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. \mforall{}[z:I:fset(\mBbbN{}) {}\mrightarrow{} a:X(I) {}\mrightarrow{} A(a)]. u = z supposing u = z
Date html generated:
2020_05_20-PM-01_52_23
Last ObjectModification:
2020_04_03-PM-08_27_54
Theory : cubical!type!theory
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