Nuprl Lemma : A-face-compatible_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[f1,f2:A-face(X;A;I;alpha)].
(A-face-compatible(X;A;I;alpha;f1;f2) ∈ ℙ)
Proof
Definitions occuring in Statement :
A-face-compatible: A-face-compatible(X;A;I;alpha;f1;f2),
A-face: A-face(X;A;I;alpha),
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
A-face-compatible: A-face-compatible(X;A;I;alpha;f1;f2),
A-face: A-face(X;A;I;alpha),
spreadn: spread3,
nameset: nameset(L),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
squash: ↓T,
all: ∀x:A. B[x],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
face-map_wf2,
list-diff_wf,
coordinate_name_wf,
cname_deq_wf,
cons_wf,
nil_wf,
not_wf,
equal_wf,
cubical-type-at_wf,
cube-set-restriction_wf,
name-comp_wf,
cubical-type-ap-morph_wf,
subtype_rel-equal,
squash_wf,
true_wf,
cube-set-restriction-comp,
iff_weakening_equal,
I-cube_wf,
name-morph_wf,
list_wf,
face-maps-commute,
A-face_wf,
cubical-type_wf,
cubical-set_wf,
subtype_rel_self,
subtype_rel_wf,
list-diff2-sym,
list-diff2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
applyEquality,
because_Cache,
functionEquality,
independent_isectElimination,
instantiate,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)]. \mforall{}[f1,f2:A-face(X;A;I;alpha)].
(A-face-compatible(X;A;I;alpha;f1;f2) \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-10_17_48
Last ObjectModification:
2017_07_28-AM-11_20_29
Theory : cubical!sets
Home
Index