Nuprl Lemma : member-from-upto
∀n,m:ℤ. ∀k:{x:ℤ| (n ≤ x) ∧ x < m} . (k ∈ [n, m))
Proof
Definitions occuring in Statement :
from-upto: [n, m),
l_member: (x ∈ l),
less_than: a < b,
le: A ≤ B,
all: ∀x:A. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
l_member: (x ∈ l),
exists: ∃x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
nat: ℕ,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
decidable__le,
subtract_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
length-from-upto,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
select-from-upto,
lelt_wf,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
length_wf,
from-upto_wf,
equal-wf-base-T,
select_wf,
nat_properties,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
setElimination,
thin,
rename,
cut,
sqequalHypSubstitution,
productElimination,
dependent_set_memberEquality,
because_Cache,
introduction,
extract_by_obid,
dependent_functionElimination,
natural_numberEquality,
isectElimination,
hypothesisEquality,
hypothesis,
unionElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
addEquality,
productEquality,
setEquality
Latex:
\mforall{}n,m:\mBbbZ{}. \mforall{}k:\{x:\mBbbZ{}| (n \mleq{} x) \mwedge{} x < m\} . (k \mmember{} [n, m))
Date html generated:
2017_04_17-AM-07_55_16
Last ObjectModification:
2017_02_27-PM-04_26_35
Theory : list_1
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