Nuprl Lemma : igrp_properties
∀[g:IGroup]. Inverse(|g|;*;e;~)
Proof
Definitions occuring in Statement : 
igrp: IGroup
, 
grp_inv: ~
, 
grp_id: e
, 
grp_op: *
, 
grp_car: |g|
, 
inverse: Inverse(T;op;id;inv)
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
igrp: IGroup
, 
imon: IMonoid
, 
sq_stable: SqStable(P)
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
inverse: Inverse(T;op;id;inv)
, 
and: P ∧ Q
Lemmas referenced : 
igrp_wf, 
grp_inv_wf, 
grp_id_wf, 
grp_op_wf, 
grp_car_wf, 
sq_stable__inverse
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
lemma_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
sqequalRule, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
isect_memberEquality, 
productElimination, 
independent_pairEquality, 
axiomEquality
Latex:
\mforall{}[g:IGroup].  Inverse(|g|;*;e;\msim{})
Date html generated:
2016_05_15-PM-00_07_56
Last ObjectModification:
2016_01_15-PM-11_06_21
Theory : groups_1
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