Nuprl Lemma : imon_all_properties
∀[g:IMonoid]. (Assoc(|g|;*) ∧ Ident(|g|;*;e))
Proof
Definitions occuring in Statement :
imon: IMonoid,
grp_id: e,
grp_op: *,
grp_car: |g|,
ident: Ident(T;op;id),
assoc: Assoc(T;op),
uall: ∀[x:A]. B[x],
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid,
and: P ∧ Q,
assoc: Assoc(T;op),
ident: Ident(T;op;id),
monoid_p: IsMonoid(T;op;id),
cand: A c∧ B
Lemmas referenced :
imon_properties,
grp_car_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
independent_pairFormation
Latex:
\mforall{}[g:IMonoid]. (Assoc(|g|;*) \mwedge{} Ident(|g|;*;e))
Date html generated:
2016_05_15-PM-00_06_40
Last ObjectModification:
2015_12_26-PM-11_47_16
Theory : groups_1
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