Nuprl Lemma : iabmonoid_properties
∀[g:IAbMonoid]. Comm(|g|;*)
Proof
Definitions occuring in Statement :
iabmonoid: IAbMonoid,
grp_op: *,
grp_car: |g|,
comm: Comm(T;op),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iabmonoid: IAbMonoid,
imon: IMonoid,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
comm: Comm(T;op)
Lemmas referenced :
iabmonoid_wf,
grp_op_wf,
grp_car_wf,
sq_stable__comm
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,
axiomEquality
Latex:
\mforall{}[g:IAbMonoid]. Comm(|g|;*)
Date html generated:
2016_05_15-PM-00_07_15
Last ObjectModification:
2016_01_15-PM-11_06_29
Theory : groups_1
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