Nuprl Lemma : abmonoid_comm
∀[g:IAbMonoid]. ∀[a,b:|g|]. ((a * b) = (b * a) ∈ |g|)
Proof
Definitions occuring in Statement :
iabmonoid: IAbMonoid,
grp_op: *,
grp_car: |g|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
comm: Comm(T;op),
uall: ∀[x:A]. B[x],
member: t ∈ T,
iabmonoid: IAbMonoid,
imon: IMonoid
Lemmas referenced :
grp_car_wf,
iabmonoid_wf,
iabmonoid_properties
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
setElimination,
rename
Latex:
\mforall{}[g:IAbMonoid]. \mforall{}[a,b:|g|]. ((a * b) = (b * a))
Date html generated:
2016_05_15-PM-00_07_17
Last ObjectModification:
2015_12_26-PM-11_46_45
Theory : groups_1
Home
Index