Nuprl Lemma : select_fun_ap_is_last1
∀[g:Base]. ∀[m1,m2:ℕ].
(select_fun_ap(partial_ap_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2 + 1;m2) ~ select_fun_last(g;m1 + m2))
Proof
Definitions occuring in Statement :
select_fun_last: select_fun_last(g;m),
select_fun_ap: select_fun_ap(g;n;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
select_fun_last: select_fun_last(g;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
select_fun_ap: select_fun_ap(g;n;m),
uimplies: b supposing a,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
mk_lambdas: mk_lambdas(F;m),
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
mk_lambdas_fun: mk_lambdas_fun(F;m),
mk_lambdas-fun: mk_lambdas-fun(F;G;n;m),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
less_than': less_than'(a;b),
true: True,
bfalse: ff,
assert: ↑b
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
primrec0_lemma,
mk_lambdas_fun_lambdas,
decidable__le,
intformand_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
le_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
bfalse_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
le_int_wf,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
btrue_wf,
mk_lambdas_compose,
add-commutes,
nat_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_set_memberEquality,
addEquality,
independent_pairFormation,
productElimination,
lambdaFormation,
equalityElimination,
promote_hyp,
sqequalAxiom
Latex:
\mforall{}[g:Base]. \mforall{}[m1,m2:\mBbbN{}].
(select\_fun\_ap(partial\_ap\_gen(g;(m1 + m2) + 1;m1;m2 + 1);m2 + 1;m2) \msim{} select\_fun\_last(g;m1 + m2))
Date html generated:
2017_10_01-AM-08_41_04
Last ObjectModification:
2017_07_26-PM-04_28_23
Theory : untyped!computation
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