Nuprl Lemma : oal_merge_comm
∀a:LOSet. ∀b:AbDMon. ∀ps,qs:|oal(a;b)|. ((ps ++ qs) = (qs ++ ps) ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
oalist: oal(a;b),
all: ∀x:A. B[x],
equal: s = t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
squash: ↓T,
prop: ℙ,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
dset_list: s List,
set_prod: s × t
Lemmas referenced :
lookups_same_a,
oal_merge_wf2,
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf,
equal_wf,
squash_wf,
true_wf,
grp_car_wf,
lookup_merge,
iff_weakening_equal,
infix_ap_wf,
dset_of_mon_wf0,
grp_op_wf,
lookup_wf,
grp_id_wf,
abmonoid_comm,
abmonoid_subtype_iabmonoid,
abdmonoid_abmonoid,
subtype_rel_transitivity,
abmonoid_wf,
iabmonoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
isectElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
functionEquality,
instantiate
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps,qs:|oal(a;b)|. ((ps ++ qs) = (qs ++ ps))
Date html generated:
2017_10_01-AM-10_02_52
Last ObjectModification:
2017_03_03-PM-01_05_27
Theory : polynom_2
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