Nuprl Lemma : fills-faces_wf
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[bx:X(I)]. ∀[L:I-face(X;I) List]. (fills-faces(X;I;bx;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
fills-faces: fills-faces(X;I;bx;L),
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,
fills-faces: fills-faces(X;I;bx;L),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_all_wf2,
I-face_wf,
is-face_wf,
l_member_wf,
list_wf,
I-cube_wf,
coordinate_name_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,
lambdaEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[bx:X(I)]. \mforall{}[L:I-face(X;I) List]. (fills-faces(X;I;bx;L) \mmember{} \mBbbP{})
Date html generated:
2016_06_16-PM-05_50_58
Last ObjectModification:
2015_12_28-PM-04_30_01
Theory : cubical!sets
Home
Index