Nuprl Lemma : mon_assoc
∀[g:IMonoid]. ∀[a,b,c:|g|]. ((a * (b * c)) = ((a * b) * c) ∈ |g|)
Proof
Definitions occuring in Statement :
imon: IMonoid,
grp_op: *,
grp_car: |g|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
assoc: Assoc(T;op),
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid,
monoid_p: IsMonoid(T;op;id),
and: P ∧ Q
Lemmas referenced :
imon_properties,
grp_car_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
productElimination
Latex:
\mforall{}[g:IMonoid]. \mforall{}[a,b,c:|g|]. ((a * (b * c)) = ((a * b) * c))
Date html generated:
2016_05_15-PM-00_06_44
Last ObjectModification:
2015_12_26-PM-11_47_10
Theory : groups_1
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