Nuprl Lemma : sg-op-inv
∀[sg:s-Group]. ∀[x:Point]. (x x^-1) ≡ 1
Proof
Definitions occuring in Statement :
sg-op: (x y),
sg-inv: x^-1,
sg-id: 1,
s-group: s-Group,
ss-eq: x ≡ y,
ss-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
false: False,
not: ¬A,
ss-eq: x ≡ y,
sq_stable: SqStable(P),
sg-op: (x y),
sg-inv: x^-1,
sg-id: 1,
squash: ↓T,
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,
sg-id_wf,
sg-inv_wf,
sg-op_wf,
sq_stable__ss-eq,
or_wf,
ss-sep_wf,
ss-eq_wf,
all_wf,
ss-point_wf,
subtype_rel_self
Rules used in proof :
voidElimination,
isect_memberEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
imageElimination,
baseClosed,
imageMemberEquality,
Error :applyLambdaEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
functionExtensionality,
lambdaEquality,
productEquality,
because_Cache,
setEquality,
functionEquality,
isectElimination,
extract_by_obid,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
hypothesisEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x:Point]. (x x\^{}-1) \mequiv{} 1
Date html generated:
2016_11_08-AM-09_11_40
Last ObjectModification:
2016_11_02-PM-07_04_31
Theory : inner!product!spaces
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