Nuprl Lemma : mon_ident
∀[g:IMonoid]. ∀[a:|g|]. (((a * e) = a ∈ |g|) ∧ ((e * a) = a ∈ |g|))
Proof
Definitions occuring in Statement :
imon: IMonoid,
grp_id: e,
grp_op: *,
grp_car: |g|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
ident: Ident(T;op;id),
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
imon: IMonoid,
monoid_p: IsMonoid(T;op;id)
Lemmas referenced :
grp_car_wf,
imon_wf,
imon_properties
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
setElimination,
rename
Latex:
\mforall{}[g:IMonoid]. \mforall{}[a:|g|]. (((a * e) = a) \mwedge{} ((e * a) = a))
Date html generated:
2016_05_15-PM-00_06_42
Last ObjectModification:
2015_12_26-PM-11_47_15
Theory : groups_1
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