Nuprl Lemma : sd_ordered_count
∀s:QOSet. ∀as:|s| List. ((↑sd_ordered(as)) ⇒ (∀c:|s|. ((c #∈ as) ≤ 1)))
Proof
Definitions occuring in Statement :
sd_ordered: sd_ordered(as),
count: a #∈ as,
list: T List,
assert: ↑b,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
qoset: QOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
qoset: QOSet,
dset: DSet,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
ge: i ≥ j ,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
band_mon: <𝔹,∧b>,
grp_car: |g|,
pi1: fst(t),
so_apply: x[s1;s2],
guard: {T},
uiff: uiff(P;Q),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
abmonoid: AbMon,
mon: Mon,
b2i: b2i(b),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_induction,
set_car_wf,
assert_wf,
sd_ordered_wf,
all_wf,
le_wf,
count_wf,
list_wf,
le_weakening2,
nil_wf,
length_nil,
non_neg_length,
count_bounds,
length_of_nil_lemma,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
count_nil_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
assert_functionality_wrt_uiff,
cons_wf,
mon_htfor_wf,
band_mon_wf,
ball_wf,
set_blt_wf,
bool_wf,
sd_ordered_char,
mon_htfor_cons_lemma,
assert_of_band,
grp_car_wf,
abmonoid_wf,
qoset_wf,
count_cons_lemma,
set_eq_wf,
uiff_transitivity,
equal-wf-T-base,
equal_wf,
eqtt_to_assert,
assert_of_dset_eq,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
squash_wf,
true_wf,
add_functionality_wrt_eq,
dset_wf,
iff_weakening_equal,
before_all_imp_count_zero,
decidable__le,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
dependent_functionElimination,
hypothesisEquality,
natural_numberEquality,
independent_functionElimination,
independent_isectElimination,
voidEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
computeAll,
applyEquality,
equalityElimination,
baseClosed,
impliesFunctionality,
imageElimination,
imageMemberEquality,
universeEquality,
addEquality
Latex:
\mforall{}s:QOSet. \mforall{}as:|s| List. ((\muparrow{}sd\_ordered(as)) {}\mRightarrow{} (\mforall{}c:|s|. ((c \#\mmember{} as) \mleq{} 1)))
Date html generated:
2017_10_01-AM-10_01_36
Last ObjectModification:
2017_03_03-PM-01_04_04
Theory : polynom_2
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