Nuprl Lemma : omral_action_wf
∀g:OCMon. ∀r:CDRng. ∀v:|r|. ∀ps:|omral(g;r)|. (v ⋅⋅ ps ∈ |omral(g;r)|)
Proof
Definitions occuring in Statement :
omral_action: v ⋅⋅ ps,
omralist: omral(g;r),
all: ∀x:A. B[x],
member: t ∈ T,
cdrng: CDRng,
rng_car: |r|,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
omral_action: v ⋅⋅ ps,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
subtype_rel: A ⊆r B,
dset: DSet,
cdrng: CDRng,
crng: CRng,
rng: Rng
Lemmas referenced :
omral_scale_wf2,
grp_id_wf,
set_car_wf,
omralist_wf,
dset_wf,
rng_car_wf,
cdrng_wf,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
hypothesis,
applyEquality,
lambdaEquality
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}v:|r|. \mforall{}ps:|omral(g;r)|. (v \mcdot{}\mcdot{} ps \mmember{} |omral(g;r)|)
Date html generated:
2016_05_16-AM-08_26_38
Last ObjectModification:
2015_12_28-PM-06_38_05
Theory : polynom_3
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