Nuprl Lemma : callbyvalueall-seq-fun1
∀[L,K,G,F:Top]. ∀[n,m:ℕ]. ∀[k1,k2:ℕn + 1].
(callbyvalueall-seq(λi.if i <z k1 then L[i] else K[i] fi ;G;F;n;m) ~ callbyvalueall-seq(λi.if i <z k2
then L[i]
else K[i]
fi ;G;F;n;m))
Proof
Definitions occuring in Statement :
callbyvalueall-seq: callbyvalueall-seq(L;G;F;n;m),
int_seg: {i..j-},
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],
lambda: λx.A[x],
add: n + m,
natural_number: $n,
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],
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
sq_type: SQType(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
Lemmas referenced :
decidable__le,
subtract_wf,
int_seg_properties,
nat_properties,
full-omega-unsat,
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,
int_seg_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,
lt_int_wf,
assert_of_lt_int,
decidable__lt,
lelt_wf,
top_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
unionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
isectElimination,
natural_numberEquality,
addEquality,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
intWeakElimination,
lambdaFormation,
sqequalAxiom,
equalityElimination,
promote_hyp,
isect_memberFormation
Latex:
\mforall{}[L,K,G,F:Top]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[k1,k2:\mBbbN{}n + 1].
(callbyvalueall-seq(\mlambda{}i.if i <z k1 then L[i] else K[i] fi ;G;F;n;m)
\msim{} callbyvalueall-seq(\mlambda{}i.if i <z k2 then L[i] else K[i] fi ;G;F;n;m))
Date html generated:
2018_05_21-PM-06_21_56
Last ObjectModification:
2018_05_19-PM-05_28_34
Theory : untyped!computation
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