Nuprl Lemma : length-from-upto
∀[n,m:ℤ]. (||[n, m)|| ~ if n <z m then m - n else 0 fi )
Proof
Definitions occuring in Statement :
from-upto: [n, m),
length: ||as||,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
from-upto: [n, m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
decidable: Dec(P),
or: P ∨ Q,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b),
has-value: (a)↓
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,
subtype_base_sq,
nat_wf,
set_subtype_base,
int_subtype_base,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
length_of_cons_lemma,
decidable__equal_int,
itermSubtract_wf,
int_term_value_subtract_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
length_of_nil_lemma,
intformnot_wf,
intformeq_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
false_wf,
decidable__le,
value-type-has-value,
int-value-type,
itermAdd_wf,
int_term_value_add_lemma,
non_neg_length,
from-upto_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
instantiate,
cumulativity,
because_Cache,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
addEquality,
dependent_set_memberEquality,
promote_hyp,
callbyvalueReduce,
isect_memberFormation,
setEquality,
productEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. (||[n, m)|| \msim{} if n <z m then m - n else 0 fi )
Date html generated:
2017_04_17-AM-07_53_25
Last ObjectModification:
2017_02_27-PM-04_27_34
Theory : list_1
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