Nuprl Lemma : face-image_wf
∀[X:CubicalSet]. ∀[I,K:Cname List]. ∀[f:name-morph(I;K)]. ∀[face:I-face(X;I)].
face-image(X;I;K;f;face) ∈ I-face(X;K) supposing ↑isname(f (fst(face)))
Proof
Definitions occuring in Statement :
face-image: face-image(X;I;K;f;face),
I-face: I-face(X;I),
cubical-set: CubicalSet,
name-morph: name-morph(I;J),
isname: isname(z),
coordinate_name: Cname,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
member: t ∈ T,
apply: f a
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
face-image: face-image(X;I;K;f;face),
I-face: I-face(X;I),
spreadn: spread3,
pi1: fst(t),
name-morph: name-morph(I;J),
prop: ℙ,
nameset: nameset(L),
uiff: uiff(P;Q),
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
assert_wf,
isname_wf,
I-face_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
cubical-set_wf,
assert-isname,
l_member_wf,
name-morph_subtype_remove1,
cube-set-restriction_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
nameset_wf,
int_seg_wf,
I-cube_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
setElimination,
rename,
because_Cache,
dependent_set_memberEquality,
independent_isectElimination,
dependent_pairEquality,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
productEquality,
natural_numberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I,K:Cname List]. \mforall{}[f:name-morph(I;K)]. \mforall{}[face:I-face(X;I)].
face-image(X;I;K;f;face) \mmember{} I-face(X;K) supposing \muparrow{}isname(f (fst(face)))
Date html generated:
2016_06_16-PM-05_51_16
Last ObjectModification:
2015_12_28-PM-04_29_51
Theory : cubical!sets
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