Nuprl Lemma : sg-inv-id
∀[sg:s-Group]. 1^-1 ≡ 1
Proof
Definitions occuring in Statement : 
s-group: s-Group
, 
sg-inv: x^-1
, 
sg-id: 1
, 
ss-eq: x ≡ y
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
ss-eq: x ≡ y
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
uimplies: b supposing a
Lemmas referenced : 
ss-sep_wf, 
s-group_subtype1, 
sg-inv_wf, 
sg-id_wf, 
s-group_wf, 
sg-op-id, 
sg-inv-unique
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
lambdaEquality, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
voidElimination, 
extract_by_obid, 
isectElimination, 
applyEquality, 
hypothesis, 
independent_isectElimination
Latex:
\mforall{}[sg:s-Group].  1\^{}-1  \mequiv{}  1
Date html generated:
2017_10_02-PM-03_25_02
Last ObjectModification:
2017_06_22-PM-06_00_40
Theory : constructive!algebra
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