Nuprl Lemma : sg-action_wf
∀[g:s-Group]. ∀[n:SeparationSpace]. (sg-action(g;n) ∈ Type)
Proof
Definitions occuring in Statement :
sg-action: sg-action(g;n),
s-group: s-Group,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sg-action: sg-action(g;n),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
so_lambda: λ2x.t[x],
s-group: s-Group,
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
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,
all_wf,
ss-eq_wf,
sg-op_wf,
sg-id_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
because_Cache,
productEquality,
lambdaEquality,
functionExtensionality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[g:s-Group]. \mforall{}[n:SeparationSpace]. (sg-action(g;n) \mmember{} Type)
Date html generated:
2017_10_02-PM-03_25_31
Last ObjectModification:
2017_07_03-PM-01_49_37
Theory : constructive!algebra
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