Nuprl Lemma : face-compatible_wf
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[f1,f2:I-face(X;I)]. (face-compatible(X;I;f1;f2) ∈ ℙ)
Proof
Definitions occuring in Statement :
face-compatible: face-compatible(X;I;f1;f2),
I-face: I-face(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,
face-compatible: face-compatible(X;I;f1;f2),
I-face: I-face(X;I),
spreadn: spread3,
implies: P ⇒ Q,
prop: ℙ,
nameset: nameset(L),
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
not_wf,
equal_wf,
coordinate_name_wf,
I-cube_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
cube-set-restriction_wf,
I-face_wf,
list_wf,
cubical-set_wf,
face-map_wf2,
name-morph_wf,
subtype_rel_self,
subtype_rel_wf,
squash_wf,
true_wf,
list-diff2,
iff_weakening_equal,
list-diff2-sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
functionEquality,
extract_by_obid,
isectElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
applyEquality,
natural_numberEquality,
lambdaEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[f1,f2:I-face(X;I)]. (face-compatible(X;I;f1;f2) \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-10_17_36
Last ObjectModification:
2017_07_28-AM-11_20_23
Theory : cubical!sets
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