Nuprl Lemma : oalist_subtype_oal_mon
∀a:LOSet. ∀b:AbDMon. (|oal(a;b)| ⊆r |oal_mon(a;b)|)
Proof
Definitions occuring in Statement :
oal_mon: oal_mon(a;b),
oalist: oal(a;b),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
abdmonoid: AbDMon,
grp_car: |g|,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
oal_mon: oal_mon(a;b),
grp_car: |g|,
uall: ∀[x:A]. B[x],
dset: DSet
Lemmas referenced :
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
hypothesisEquality,
cut,
lemma_by_obid,
isectElimination,
thin,
dependent_functionElimination,
hypothesis,
applyEquality,
setElimination,
rename
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. (|oal(a;b)| \msubseteq{}r |oal\_mon(a;b)|)
Date html generated:
2016_05_16-AM-08_18_36
Last ObjectModification:
2015_12_28-PM-06_26_34
Theory : polynom_2
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