Nuprl Lemma : oal_bpos_wf
∀s:LOSet. ∀g:AbDMon. ∀ps:|oal(s;g)|. (pos(ps) ∈ 𝔹)
Proof
Definitions occuring in Statement :
oal_bpos: pos(ps),
oalist: oal(a;b),
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oal_bpos: pos(ps),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
band: p ∧b q,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
prop: ℙ,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon
Lemmas referenced :
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf,
bnot_wf,
oal_null_wf,
bool_wf,
iff_transitivity,
equal-wf-T-base,
assert_wf,
not_wf,
equal_wf,
oal_nil_wf,
iff_weakening_uiff,
eqtt_to_assert,
assert_of_bnot,
assert_of_oal_null,
eqff_to_assert,
grp_blt_wf,
grp_id_wf,
oal_lv_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache,
independent_pairFormation,
impliesFunctionality,
productElimination,
voidElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. \mforall{}ps:|oal(s;g)|. (pos(ps) \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-10_03_58
Last ObjectModification:
2017_03_03-PM-01_07_10
Theory : polynom_2
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