Nuprl Lemma : sq_stable__face-compatible
∀X:CubicalSet. ∀I:Cname List. ∀f1,f2:I-face(X;I).  SqStable(face-compatible(X;I;f1;f2))
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
, 
sq_stable: SqStable(P)
, 
all: ∀x:A. B[x]
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
I-face: I-face(X;I)
, 
face-compatible: face-compatible(X;I;f1;f2)
, 
spreadn: spread3, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
nameset: nameset(L)
, 
subtype_rel: A ⊆r B
, 
true: True
, 
squash: ↓T
, 
prop: ℙ
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
I-face_wf, 
list_wf, 
coordinate_name_wf, 
cubical-set_wf, 
face-map_wf2, 
list-diff_wf, 
cname_deq_wf, 
cons_wf, 
nil_wf, 
name-morph_wf, 
subtype_rel_self, 
subtype_rel_wf, 
squash_wf, 
true_wf, 
list-diff2, 
iff_weakening_equal, 
list-diff2-sym, 
sq_stable__all, 
not_wf, 
equal_wf, 
I-cube_wf, 
cube-set-restriction_wf, 
sq_stable__equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
applyEquality, 
because_Cache, 
natural_numberEquality, 
lambdaEquality, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
imageMemberEquality, 
baseClosed, 
independent_isectElimination, 
independent_functionElimination
Latex:
\mforall{}X:CubicalSet.  \mforall{}I:Cname  List.  \mforall{}f1,f2:I-face(X;I).    SqStable(face-compatible(X;I;f1;f2))
Date html generated:
2018_05_23-PM-06_32_12
Last ObjectModification:
2018_05_20-PM-04_21_37
Theory : cubical!sets
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