Nuprl Lemma : select-from-upto
∀[n,m:ℤ]. ∀[k:ℕm - n]. ([n, m)[k] ~ n + k)
Proof
Definitions occuring in Statement :
from-upto: [n, m),
select: L[n],
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
add: 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,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
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),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
cons: [a / b],
has-value: (a)↓,
subtype_rel: A ⊆r B
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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,
int_seg_wf,
subtract_wf,
le_wf,
subtract-1-ge-0,
nat_wf,
int_seg_properties,
itermSubtract_wf,
int_term_value_subtract_lemma,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
stuck-spread,
istype-base,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__equal_int,
int_subtype_base,
add-zero,
value-type-has-value,
int-value-type,
decidable__le,
itermAdd_wf,
int_term_value_add_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__lt,
select-cons-tl,
select_wf,
from-upto_wf,
length-from-upto,
satisfiable-full-omega-tt
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :universeIsType,
axiomSqEquality,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
productElimination,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
Error :equalityIsType1,
promote_hyp,
instantiate,
cumulativity,
because_Cache,
baseClosed,
intEquality,
callbyvalueReduce,
addEquality,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
applyEquality,
Error :isect_memberFormation_alt,
computeAll,
voidEquality,
isect_memberEquality,
lambdaEquality,
dependent_pairFormation,
dependent_set_memberEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[k:\mBbbN{}m - n]. ([n, m)[k] \msim{} n + k)
Date html generated:
2019_06_20-PM-01_34_11
Last ObjectModification:
2018_10_04-PM-02_28_32
Theory : list_1
Home
Index