Nuprl Lemma : cubical-term-equal
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. ∀[z:I:(Cname List) ⟶ a:X(I) ⟶ ((fst(A)) I a)].
u = z ∈ {X ⊢ _:A} supposing u = z ∈ (I:(Cname List) ⟶ a:X(I) ⟶ ((fst(A)) I a))
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
cubical-type: {X ⊢ _},
pi1: fst(t),
cubical-term: {X ⊢ _:AF},
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cubical-term_wf,
cubical-type_wf,
cubical-set_wf,
list_wf,
coordinate_name_wf,
I-cube_wf,
equal_wf,
all_wf,
name-morph_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
lambdaFormation,
setElimination,
rename,
productElimination,
sqequalRule,
applyEquality,
functionExtensionality,
functionEquality,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
lambdaEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. \mforall{}[z:I:(Cname List) {}\mrightarrow{} a:X(I) {}\mrightarrow{} ((fst(A)) I a)].
u = z supposing u = z
Date html generated:
2017_10_05-AM-10_13_03
Last ObjectModification:
2017_07_28-AM-11_18_40
Theory : cubical!sets
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