Nuprl Lemma : oset_of_ocmon_wf
∀[g:OMon]. (g↓oset ∈ LOSet)
Proof
Definitions occuring in Statement :
oset_of_ocmon: g↓oset,
omon: OMon,
loset: LOSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
omon: OMon,
and: P ∧ Q,
abmonoid: AbMon,
mon: Mon,
ulinorder: UniformLinorder(T;x,y.R[x; y]),
monoid_p: IsMonoid(T;op;id),
uorder: UniformOrder(T;x,y.R[x; y]),
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
set_eq: =b,
pi2: snd(t),
prop: ℙ,
set_leq: a ≤ b,
set_le: ≤b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
upreorder: UniformPreorder(T;x,y.R[x; y])
Lemmas referenced :
omon_properties,
abmonoid_properties,
mon_properties,
omon_wf,
oset_of_ocmon_wf0,
eqfun_p_wf,
set_car_wf,
set_eq_wf,
upreorder_wf,
set_leq_wf,
uanti_sym_wf,
connex_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesis,
applyLambdaEquality,
productElimination,
setElimination,
rename,
isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
dependent_set_memberEquality,
lambdaEquality,
because_Cache,
independent_pairFormation
Latex:
\mforall{}[g:OMon]. (g\mdownarrow{}oset \mmember{} LOSet)
Date html generated:
2017_10_01-AM-08_14_35
Last ObjectModification:
2017_02_28-PM-01_58_48
Theory : groups_1
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