Nuprl Lemma : callbyvalueall_seq-combine3-0
∀[F,L1,L2:Top]. ∀[m1,m2:ℕ].
(callbyvalueall_seq(L1;λx.x;λg.callbyvalueall_seq(L2[g];λx.x;F[g];0;m2);0;m1)
~ callbyvalueall_seq(λi.if i <z m1 then L1 i else mk_lambdas_fun(λg.(L2[g] (i - m1));m1) fi ;λx.x
;λg.(F[partial_ap(g;m1 + m2;m1)] partial_ap_gen(g;m1 + m2;m1;m2));0;m1 + m2))
Proof
Definitions occuring in Statement :
partial_ap: partial_ap(g;n;m),
partial_ap_gen: partial_ap_gen(g;n;s;m),
mk_lambdas_fun: mk_lambdas_fun(F;m),
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
nat: ℕ,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
lambda: λx.A[x],
subtract: n - m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
mk_applies: mk_applies(F;G;m)
Lemmas referenced :
top_wf,
nat_wf,
primrec0_lemma,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
false_wf,
callbyvalueall_seq-combine3
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[F,L1,L2:Top]. \mforall{}[m1,m2:\mBbbN{}].
(callbyvalueall\_seq(L1;\mlambda{}x.x;\mlambda{}g.callbyvalueall\_seq(L2[g];\mlambda{}x.x;F[g];0;m2);0;m1)
\msim{} callbyvalueall\_seq(\mlambda{}i.if i <z m1 then L1 i else mk\_lambdas\_fun(\mlambda{}g.(L2[g] (i - m1));m1) fi ;\mlambda{}x.x
;\mlambda{}g.(F[partial\_ap(g;m1 + m2;m1)] partial\_ap\_gen(g;m1 + m2;m1;m2));0;m1 + m2))
Date html generated:
2016_05_15-PM-02_14_36
Last ObjectModification:
2016_01_15-PM-10_17_52
Theory : untyped!computation
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