Nuprl Lemma : I-path-morph_wf
∀X:CubicalSet. ∀A:{X ⊢ _}. ∀a,b:{X ⊢ _:A}. ∀I,K:Cname List. ∀f:name-morph(I;K). ∀alpha:X(I). ∀w:I-path(X;A;a;b;I;alpha).
(I-path-morph(X;A;I;K;f;alpha;w) ∈ I-path(X;A;a;b;K;f(alpha)))
Proof
Definitions occuring in Statement :
I-path-morph: I-path-morph(X;A;I;K;f;alpha;p),
I-path: I-path(X;A;a;b;I;alpha),
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
cube-set-restriction: f(s),
I-cube: X(I),
cubical-set: CubicalSet,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
I-path: I-path(X;A;a;b;I;alpha),
all: ∀x:A. B[x],
member: t ∈ T,
I-path-morph: I-path-morph(X;A;I;K;f;alpha;p),
uall: ∀[x:A]. B[x],
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
fresh-cname_wf,
named-path-morph_wf,
not_wf,
l_member_wf,
coordinate_name_wf,
named-path_wf,
cube-set-restriction_wf,
I-cube_wf,
name-morph_wf,
list_wf,
cubical-term_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
productElimination,
thin,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
setElimination,
rename,
independent_isectElimination,
productEquality,
setEquality
Latex:
\mforall{}X:CubicalSet. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}a,b:\{X \mvdash{} \_:A\}. \mforall{}I,K:Cname List. \mforall{}f:name-morph(I;K). \mforall{}alpha:X(I).
\mforall{}w:I-path(X;A;a;b;I;alpha).
(I-path-morph(X;A;I;K;f;alpha;w) \mmember{} I-path(X;A;a;b;K;f(alpha)))
Date html generated:
2016_06_16-PM-07_29_03
Last ObjectModification:
2015_12_28-PM-04_13_43
Theory : cubical!sets
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