Nuprl Lemma : imon_properties
∀[g:IMonoid]. IsMonoid(|g|;*;e)
Proof
Definitions occuring in Statement :
imon: IMonoid,
grp_id: e,
grp_op: *,
grp_car: |g|,
monoid_p: IsMonoid(T;op;id),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
monoid_p: IsMonoid(T;op;id),
and: P ∧ Q,
assoc: Assoc(T;op),
ident: Ident(T;op;id)
Lemmas referenced :
imon_wf,
grp_id_wf,
grp_op_wf,
grp_car_wf,
sq_stable__monoid_p
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,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[g:IMonoid]. IsMonoid(|g|;*;e)
Date html generated:
2016_05_15-PM-00_06_39
Last ObjectModification:
2016_01_15-PM-11_06_30
Theory : groups_1
Home
Index