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
Home
Index