Nuprl Lemma : callbyvalueall_seq-fun1
∀[F,G,A,B:Top]. ∀[K:ℤ ⟶ 𝔹]. ∀[n,m:ℕ].
callbyvalueall_seq(λi.if K[i] then A[i] else B[i] fi ;G;F;n;m) ~ callbyvalueall_seq(λi.B[i];G;F;n;m)
supposing ∀i:{n..m + 1-}. K[i] = ff
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 ,
bfalse: ff,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ 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},
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
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,
lelt: i ≤ j < k,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
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,
all_wf,
int_seg_wf,
equal-wf-T-base,
bool_wf,
nat_wf,
le_int_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
assert_functionality_wrt_uiff,
bfalse_wf,
decidable__lt,
lelt_wf,
squash_wf,
true_wf,
iff_weakening_equal,
top_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
unionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
isectElimination,
hypothesisEquality,
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,
applyEquality,
functionExtensionality,
baseClosed,
equalityElimination,
promote_hyp,
imageElimination,
universeEquality,
imageMemberEquality,
functionEquality,
isect_memberFormation
Latex:
\mforall{}[F,G,A,B:Top]. \mforall{}[K:\mBbbZ{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[n,m:\mBbbN{}].
callbyvalueall\_seq(\mlambda{}i.if K[i] then A[i] else B[i] fi ;G;F;n;m)
\msim{} callbyvalueall\_seq(\mlambda{}i.B[i];G;F;n;m)
supposing \mforall{}i:\{n..m + 1\msupminus{}\}. K[i] = ff
Date html generated:
2017_10_01-AM-08_42_05
Last ObjectModification:
2017_07_26-PM-04_28_57
Theory : untyped!computation
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