Nuprl Lemma : ap-action_wf
∀[g:s-Group]. ∀[n:SeparationSpace]. ∀[a:sg-action(g;n)]. ∀[h:Point]. ∀[x:Point]. (h(x) ∈ Point)
Proof
Definitions occuring in Statement :
ap-action: h(x),
sg-action: sg-action(g;n),
s-group: s-Group,
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ap-action: h(x),
sg-action: sg-action(g;n),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
ss-point_wf,
s-group-structure_subtype1,
s-group_subtype1,
subtype_rel_transitivity,
s-group_wf,
s-group-structure_wf,
separation-space_wf,
sg-action_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
instantiate,
independent_isectElimination
Latex:
\mforall{}[g:s-Group]. \mforall{}[n:SeparationSpace]. \mforall{}[a:sg-action(g;n)]. \mforall{}[h:Point]. \mforall{}[x:Point]. (h(x) \mmember{} Point)
Date html generated:
2017_10_02-PM-03_25_34
Last ObjectModification:
2017_07_03-PM-01_53_26
Theory : constructive!algebra
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