Nuprl Lemma : sd_ordered_char
ās:QOSet. āus:|s| List. sd_ordered(us) = HTFor{<š¹,ā§b>} v::vs ā us. ābw(:|s|) ā vs. (w <b v)
Proof
Definitions occuring in Statement :
sd_ordered: sd_ordered(as)
,
ball: ball,
mon_htfor: HTFor{g} h::t ā as. f[h; t]
,
list: T List
,
bool: š¹
,
all: āx:A. B[x]
,
equal: s = t ā T
,
band_mon: <š¹,ā§b>
,
qoset: QOSet
,
set_blt: a <b b
,
set_car: |p|
Definitions unfolded in proof :
all: āx:A. B[x]
,
uall: ā[x:A]. B[x]
,
member: t ā T
,
qoset: QOSet
,
dset: DSet
,
so_lambda: Ī»2x.t[x]
,
subtype_rel: A ār B
,
so_lambda: Ī»2x y.t[x; y]
,
so_apply: x[s]
,
band_mon: <š¹,ā§b>
,
grp_car: |g|
,
pi1: fst(t)
,
so_apply: x[s1;s2]
,
implies: P
ā Q
,
top: Top
,
grp_id: e
,
pi2: snd(t)
,
grp_op: *
,
infix_ap: x f y
,
prop: ā
,
squash: āT
,
bool: š¹
,
unit: Unit
,
it: ā
,
btrue: tt
,
band: p ā§b q
,
ifthenelse: if b then t else f fi
,
bfalse: ff
,
true: True
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
āā Q
,
and: P ā§ Q
,
rev_implies: P
ā Q
,
ball: ball,
uiff: uiff(P;Q)
,
or: P āØ Q
,
assert: āb
,
cons: [a / b]
,
cand: A cā§ B
,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_induction,
set_car_wf,
equal_wf,
bool_wf,
sd_ordered_wf,
mon_htfor_wf,
band_mon_wf,
ball_wf,
set_blt_wf,
list_wf,
sd_ordered_nil_lemma,
mon_htfor_nil_lemma,
btrue_wf,
sd_ordered_cons_lemma,
mon_htfor_cons_lemma,
qoset_wf,
squash_wf,
true_wf,
before_wf,
band_wf,
iff_weakening_equal,
iff_imp_equal_bool,
assert_wf,
assert_of_band,
iff_wf,
list-cases,
ball_nil_lemma,
nil_wf,
product_subtype_list,
ball_cons_lemma,
cons_wf,
before_cons_lemma,
iff_transitivity,
assert_of_set_lt,
set_lt_wf,
iff_weakening_uiff,
assert_functionality_wrt_uiff,
ball_char,
mem_wf,
set_lt_transitivity_2,
set_leq_weakening_lt,
before_nil_lemma,
mem_cons_lemma,
bor_wf,
set_eq_wf,
or_wf,
assert_of_bor,
assert_of_dset_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
equalityUniverse,
levelHypothesis,
unionElimination,
equalityElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_pairFormation,
productEquality,
addLevel,
impliesFunctionality,
promote_hyp,
hypothesis_subsumption,
orFunctionality,
inlFormation
Latex:
\mforall{}s:QOSet. \mforall{}us:|s| List. sd\_ordered(us) = HTFor\{<\mBbbB{},\mwedge{}\msubb{}>\} v::vs \mmember{} us. \mforall{}\msubb{}w(:|s|) \mmember{} vs. (w <\msubb{} v)
Date html generated:
2017_10_01-AM-10_01_32
Last ObjectModification:
2017_03_03-PM-01_04_08
Theory : polynom_2
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