Nuprl Lemma : is-face_wf
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[bx:X(I)]. ∀[f:I-face(X;I)]. (is-face(X;I;bx;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-face: is-face(X;I;bx;f),
I-face: I-face(X;I),
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,
is-face: is-face(X;I;bx;f),
subtype_rel: A ⊆r B
Lemmas referenced :
equal_wf,
I-cube_wf,
list-diff_wf,
coordinate_name_wf,
cname_deq_wf,
cons_wf,
face-dimension_wf,
nil_wf,
cube-set-restriction_wf,
face-map_wf2,
face-direction_wf,
face-cube_wf,
I-face_wf,
list_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[bx:X(I)]. \mforall{}[f:I-face(X;I)]. (is-face(X;I;bx;f) \mmember{} \mBbbP{})
Date html generated:
2016_06_16-PM-05_50_42
Last ObjectModification:
2015_12_28-PM-04_30_09
Theory : cubical!sets
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