Nuprl Lemma : sg-inv-inv
∀[sg:s-Group]. ∀[x:Point]. x^-1^-1 ≡ x
Proof
Definitions occuring in Statement :
s-group: s-Group,
sg-inv: x^-1,
ss-eq: x ≡ y,
ss-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
sg-inv-unique,
sg-inv_wf,
sg-inv-op,
ss-sep_wf,
s-group_subtype1,
ss-point_wf,
s-group_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
applyEquality,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x:Point]. x\^{}-1\^{}-1 \mequiv{} x
Date html generated:
2017_10_02-PM-03_25_01
Last ObjectModification:
2017_06_22-PM-05_59_33
Theory : constructive!algebra
Home
Index