Nuprl Lemma : from-upto_wf
∀[n,m:ℤ]. ([n, m) ∈ {x:ℤ| (n ≤ x) ∧ x < m} List)
Proof
Definitions occuring in Statement :
from-upto: [n, m),
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
le: A ≤ B,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
from-upto: [n, m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
decidable: Dec(P),
has-value: (a)↓,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
le_wf,
subtract_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
cons_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nil_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
value-type-has-value,
nat_wf,
itermAdd_wf,
int_term_value_add_lemma,
subtype_rel_list_set
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
productElimination,
setEquality,
productEquality,
because_Cache,
promote_hyp,
instantiate,
cumulativity,
callbyvalueReduce,
addEquality,
applyEquality,
isect_memberFormation,
dependent_set_memberEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. ([n, m) \mmember{} \{x:\mBbbZ{}| (n \mleq{} x) \mwedge{} x < m\} List)
Date html generated:
2017_04_17-AM-07_53_14
Last ObjectModification:
2017_02_27-PM-04_25_35
Theory : list_1
Home
Index