Nuprl Lemma : module_act_grp_hom_l
∀A:Rng. ∀m:A-Module. ∀u:m.car. IsMonHom{A↓+gp,m↓grp}(λa:|A|. m.act a u)
Proof
Definitions occuring in Statement :
module: A-Module,
grp_of_module: m↓grp,
alg_act: a.act,
alg_car: a.car,
tlambda: λx:T. b[x],
all: ∀x:A. B[x],
apply: f a,
add_grp_of_rng: r↓+gp,
rng: Rng,
rng_car: |r|,
monoid_hom_p: IsMonHom{M1,M2}(f)
Definitions unfolded in proof :
all: ∀x:A. B[x],
monoid_hom_p: IsMonHom{M1,M2}(f),
and: P ∧ Q,
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
grp_of_module: m↓grp,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
tlambda: λx:T. b[x],
grp_op: *,
pi2: snd(t),
rng_of_alg: a↓rg,
rng_car: |r|,
rng_plus: +r,
rng: Rng,
grp_id: e,
rng_zero: 0,
module: A-Module,
infix_ap: x f y
Lemmas referenced :
grp_car_wf,
add_grp_of_rng_wf,
alg_car_wf,
rng_car_wf,
module_wf,
rng_wf,
module_act_plus,
module_act_zero_l
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
dependent_functionElimination,
productElimination
Latex:
\mforall{}A:Rng. \mforall{}m:A-Module. \mforall{}u:m.car. IsMonHom\{A\mdownarrow{}+gp,m\mdownarrow{}grp\}(\mlambda{}a:|A|. m.act a u)
Date html generated:
2016_05_16-AM-07_26_59
Last ObjectModification:
2015_12_28-PM-05_07_45
Theory : algebras_1
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