Nuprl Lemma : module_action_p
∀[A:Rng]. ∀[m:A-Module].
((∀[a,b:|A|]. ∀[u:m.car]. (((a * b) m.act u) = (a m.act (b m.act u)) ∈ m.car))
∧ (∀[u:m.car]. ((1 m.act u) = u ∈ m.car)))
Proof
Definitions occuring in Statement :
module: A-Module,
alg_act: a.act,
alg_car: a.car,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
and: P ∧ Q,
equal: s = t ∈ T,
rng: Rng,
rng_one: 1,
rng_times: *,
rng_car: |r|
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
rng: Rng,
module: A-Module,
guard: {T},
action_p: IsAction(A;x;e;S;f)
Lemmas referenced :
module_properties,
alg_car_wf,
rng_car_wf,
module_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
independent_pairFormation,
independent_pairEquality
Latex:
\mforall{}[A:Rng]. \mforall{}[m:A-Module].
((\mforall{}[a,b:|A|]. \mforall{}[u:m.car]. (((a * b) m.act u) = (a m.act (b m.act u))))
\mwedge{} (\mforall{}[u:m.car]. ((1 m.act u) = u)))
Date html generated:
2016_05_16-AM-07_26_37
Last ObjectModification:
2015_12_28-PM-05_08_22
Theory : algebras_1
Home
Index