Nuprl Lemma : from-upto-shift
∀[n,m,k:ℤ]. (map(λx.(x + k);[n, m)) ~ [n + k, m + k))
Proof
Definitions occuring in Statement :
from-upto: [n, m),
map: map(f;as),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
add: n + m,
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,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P ∨ Q,
from-upto: [n, m),
has-value: (a)↓,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
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,
istype-less_than,
istype-le,
subtract_wf,
subtract-1-ge-0,
istype-nat,
from-upto-is-nil,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
map_nil_lemma,
itermAdd_wf,
int_term_value_add_lemma,
value-type-has-value,
int-value-type,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
map_cons_lemma,
eqff_to_assert,
int_subtype_base,
bool_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
list_wf,
list_subtype_base,
add-commutes,
add-associates,
add-swap,
cons_wf,
from-upto_wf,
subtype_rel_list,
le_wf,
equal_wf
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,
because_Cache,
productElimination,
unionElimination,
addEquality,
callbyvalueReduce,
intEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
Error :equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
Error :equalityIsType1,
setEquality,
productEquality,
Error :setIsType,
Error :productIsType,
isect_memberEquality,
isect_memberFormation,
voidEquality,
lambdaEquality,
dependent_pairFormation,
dependent_set_memberEquality,
lambdaFormation
Latex:
\mforall{}[n,m,k:\mBbbZ{}]. (map(\mlambda{}x.(x + k);[n, m)) \msim{} [n + k, m + k))
Date html generated:
2019_06_20-PM-01_34_02
Last ObjectModification:
2018_10_18-AM-11_38_47
Theory : list_1
Home
Index