Nuprl Lemma : select_fun_last_partial_ap1
∀[g:Top]. ∀[m:ℕ]. (select_fun_last(partial_ap(g;m + 2;m + 1);m) ~ select_fun_ap(g;m + 2;m))
Proof
Definitions occuring in Statement :
select_fun_last: select_fun_last(g;m),
select_fun_ap: select_fun_ap(g;n;m),
partial_ap: partial_ap(g;n;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
select_fun_ap: select_fun_ap(g;n;m),
partial_ap: partial_ap(g;n;m),
select_fun_last: select_fun_last(g;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,
less_than': less_than'(a;b),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
top_wf,
nat_wf,
false_wf,
mk_lambdas_fun-unroll-ite,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
le_wf,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformand_wf,
decidable__le,
mk_lambdas_fun_lambdas2,
primrec0_lemma,
primrec1_lemma,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
itermSubtract_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
int_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_set_memberEquality,
addEquality,
independent_pairFormation,
productElimination,
lambdaFormation,
sqequalAxiom
Latex:
\mforall{}[g:Top]. \mforall{}[m:\mBbbN{}]. (select\_fun\_last(partial\_ap(g;m + 2;m + 1);m) \msim{} select\_fun\_ap(g;m + 2;m))
Date html generated:
2016_05_15-PM-02_11_57
Last ObjectModification:
2016_01_15-PM-10_20_12
Theory : untyped!computation
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