Nuprl Lemma : callbyvalueall_seq-fun4
∀[L,K,G,F,J,P,Q:Top]. ∀[n,m:ℕ]. ∀[p,q:ℤ].
(callbyvalueall_seq(λi.K[if (i) < (p + q) then J[i;λout.if i - p=q then P[i;out] else Q[i]] else L[i]];G;F;n;m)
~ callbyvalueall_seq(λi.K[if (i) < (p + q) then J[i;λout.Q[i]] else L[i]];G;F;n;m))
Proof
Definitions occuring in Statement :
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
less: if (a) < (b) then c else d,
int_eq: if a=b then c else d,
lambda: λx.A[x],
subtract: n - m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
decidable__le,
subtract_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
equal_wf,
subtype_base_sq,
int_subtype_base,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
less_than_wf,
nat_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
int_eq_as_ite,
less_as_ite,
lt_int_wf,
assert_of_lt_int,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
top_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
isectElimination,
because_Cache,
natural_numberEquality,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
addEquality,
productElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
intWeakElimination,
lambdaFormation,
sqequalAxiom,
equalityElimination,
promote_hyp,
isect_memberFormation
Latex:
\mforall{}[L,K,G,F,J,P,Q:Top]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[p,q:\mBbbZ{}].
(callbyvalueall\_seq(\mlambda{}i.K[if (i) < (p + q)
then J[i;\mlambda{}out.if i - p=q then P[i;out] else Q[i]]
else L[i]];G;F;n;m) \msim{} callbyvalueall\_seq(\mlambda{}i.K[if (i) < (p + q)
then J[i;\mlambda{}out.Q[i]]
else L[i]];G;F;n;m))
Date html generated:
2017_10_01-AM-08_42_15
Last ObjectModification:
2017_07_26-PM-04_29_05
Theory : untyped!computation
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