Nuprl Lemma : simple-cbva-seq-combine
∀[F,L1,L2:Top]. ∀[m1,m2:ℕ+].
(simple-cbva-seq(L1;λout.simple-cbva-seq(L2[out];F;m2);m1) ~ simple-cbva-seq(λn.if n <z m1
then L1 n
else mk_lambdas(λout.(L2[out]
(n - m1));m1
- 1)
fi ;F;m1 + m2))
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
mk_lambdas: mk_lambdas(F;m),
nat_plus: 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 :
simple-cbva-seq: simple-cbva-seq(L;F;m),
cbva-seq: cbva-seq(L;F;m),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
itermAdd_wf,
int_term_value_add_lemma,
false_wf,
le_wf,
nat_plus_subtype_nat,
decidable__le,
intformnot_wf,
intformle_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
callbyvalueall_seq-seq,
callbyvalueall_seq-combine0,
mk_lambdas_compose,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
int_subtype_base,
decidable__equal_int,
nat_plus_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
addEquality,
because_Cache,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
approximateComputation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
dependent_set_memberEquality,
applyEquality,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[F,L1,L2:Top]. \mforall{}[m1,m2:\mBbbN{}\msupplus{}].
(simple-cbva-seq(L1;\mlambda{}out.simple-cbva-seq(L2[out];F;m2);m1)
\msim{} simple-cbva-seq(\mlambda{}n.if n <z m1 then L1 n else mk\_lambdas(\mlambda{}out.(L2[out] (n - m1));m1 - 1) fi ;F;m1
+ m2))
Date html generated:
2018_05_21-PM-06_23_49
Last ObjectModification:
2018_05_19-PM-05_32_05
Theory : untyped!computation
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