Nuprl Lemma : from-upto-sorted
∀a,b:ℤ. sorted-by(λx,y. x < y;[a, b))
Proof
Definitions occuring in Statement :
from-upto: [n, m),
sorted-by: sorted-by(R;L),
less_than: a < b,
all: ∀x:A. B[x],
lambda: λx.A[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
sorted-by: sorted-by(R;L),
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
and: P ∧ Q,
prop: ℙ,
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
select-from-upto,
int_term_value_add_lemma,
itermAdd_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
itermConstant_wf,
intformle_wf,
not_wf,
bnot_wf,
assert_wf,
int_formula_prop_wf,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
int_seg_properties,
lt_int_wf,
subtract_wf,
lelt_wf,
length-from-upto,
from-upto_wf,
less_than_wf,
le_wf,
and_wf,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
setEquality,
intEquality,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
addEquality,
instantiate,
cumulativity,
independent_functionElimination,
impliesFunctionality
Latex:
\mforall{}a,b:\mBbbZ{}. sorted-by(\mlambda{}x,y. x < y;[a, b))
Date html generated:
2016_05_14-PM-02_02_44
Last ObjectModification:
2016_01_15-AM-08_07_47
Theory : list_1
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