Nuprl Lemma : permutation-ss_wf
∀[ss:SeparationSpace]. (permutation-ss(ss) ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
permutation-ss: permutation-ss(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
fun-ss: A ⟶ ss,
btrue: tt,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-ss: mk-ss,
prod-ss: ss1 × ss2,
record-select: r.x,
ss-point: Point,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
permutation-ss: permutation-ss(ss),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-eq_wf,
all_wf,
subtype_rel_self,
ss-point_wf,
fun-ss_wf,
prod-ss_wf,
set-ss_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionEquality,
productEquality,
applyEquality,
spreadEquality,
lambdaEquality,
hypothesis,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. (permutation-ss(ss) \mmember{} SeparationSpace)
Date html generated:
2016_11_08-AM-09_12_40
Last ObjectModification:
2016_11_03-AM-00_20_59
Theory : inner!product!spaces
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