Nuprl Lemma : cubical-term-equal2
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[u,z:{X ⊢ _:A}].
u = z ∈ {X ⊢ _:A} supposing ∀I:Cname List. ∀a:X(I). ((u I a) = (z I a) ∈ ((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),
all: ∀x:A. B[x],
apply: f a,
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
guard: {T}
Lemmas referenced :
cubical-term_wf,
cubical-type_wf,
cubical-set_wf,
I-cube_wf,
list_wf,
coordinate_name_wf,
all_wf,
equal_wf,
name-morph_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
setElimination,
rename,
productElimination,
sqequalRule,
applyEquality,
introduction,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
functionExtensionality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u,z:\{X \mvdash{} \_:A\}].
u = z supposing \mforall{}I:Cname List. \mforall{}a:X(I). ((u I a) = (z I a))
Date html generated:
2016_06_16-PM-05_40_18
Last ObjectModification:
2015_12_28-PM-04_35_33
Theory : cubical!sets
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