Nuprl Lemma : sg-inv_wf
∀[sg:s-Group]. ∀[x:Point]. (x^-1 ∈ Point)
Proof
Definitions occuring in Statement :
sg-inv: x^-1,
s-group: s-Group,
ss-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
sg-inv: x^-1,
or: P ∨ Q,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
s-group: s-Group,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
s-group_wf,
s-group_subtype1,
or_wf,
ss-sep_wf,
ss-eq_wf,
all_wf,
ss-point_wf,
subtype_rel_self
Rules used in proof :
isect_memberEquality,
axiomEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
functionExtensionality,
lambdaEquality,
productEquality,
because_Cache,
setEquality,
functionEquality,
isectElimination,
extract_by_obid,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x:Point]. (x\^{}-1 \mmember{} Point)
Date html generated:
2016_11_08-AM-09_11_30
Last ObjectModification:
2016_11_02-PM-06_51_48
Theory : inner!product!spaces
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