Nuprl Lemma : path-eq_weakening
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[a,b:{X ⊢ _:A}]. ∀[I:Cname List]. ∀[alpha:X(I)].
∀p,q:I-path(X;A;a;b;I;alpha). path-eq(X;A;I;alpha;p;q) supposing p = q ∈ I-path(X;A;a;b;I;alpha)
Proof
Definitions occuring in Statement :
path-eq: path-eq(X;A;I;alpha;p;q),
I-path: I-path(X;A;a;b;I;alpha),
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],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
prop: ℙ,
guard: {T},
refl: Refl(T;x,y.E[x; y])
Lemmas referenced :
path-eq-equiv,
equal_wf,
I-path_wf,
I-cube_wf,
list_wf,
coordinate_name_wf,
cubical-term_wf,
cubical-type_wf,
cubical-set_wf,
and_wf,
path-eq_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
lambdaFormation,
axiomEquality,
rename,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
sqequalRule,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
lambdaEquality,
setElimination,
setEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a,b:\{X \mvdash{} \_:A\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)].
\mforall{}p,q:I-path(X;A;a;b;I;alpha). path-eq(X;A;I;alpha;p;q) supposing p = q
Date html generated:
2016_10_28-PM-00_14_07
Last ObjectModification:
2016_07_12-PM-00_40_59
Theory : cubical!sets
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