Nuprl Lemma : test-mutual-corec-ext
test-mutual-corec() ≡ λi.if (i =z 0)
then Unit + (test-mutual-corec() 0 × ((test-mutual-corec() 1) List))
else Unit + (test-mutual-corec() 1 × ((test-mutual-corec() 0) List))
fi
Proof
Definitions occuring in Statement :
test-mutual-corec: test-mutual-corec(),
list: T List,
k-ext: A ≡ B,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
unit: Unit,
apply: f a,
lambda: λx.A[x],
product: x:A × B[x],
union: left + right,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
so_apply: x[s],
k-monotone: k-Monotone(T.F[T]),
k-subtype: A ⊆ B,
decidable: Dec(P),
eq_int: (i =z j),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
test-mutual-corec: test-mutual-corec()
Lemmas referenced :
mutual-corec-ext2,
false_wf,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
unit_wf2,
int_seg_wf,
lelt_wf,
list_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
decidable__equal_int,
int_subtype_base,
int_seg_properties,
subtype_rel_union,
subtype_rel_product,
subtype_rel_list,
int_seg_subtype,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
k-subtype_wf,
strong-continuous-union,
continuous-constant,
strong-continuous-product,
continuous-id,
strong-continuous-list,
subtype_rel_weakening,
nat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
unionEquality,
productEquality,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
functionEquality,
universeEquality,
isect_memberFormation,
intEquality,
hypothesis_subsumption,
addEquality,
approximateComputation,
int_eqEquality,
isect_memberEquality,
voidEquality,
axiomEquality,
isectEquality
Latex:
test-mutual-corec() \mequiv{} \mlambda{}i.if (i =\msubz{} 0)
then Unit + (test-mutual-corec() 0 \mtimes{} ((test-mutual-corec() 1) List))
else Unit + (test-mutual-corec() 1 \mtimes{} ((test-mutual-corec() 0) List))
fi
Date html generated:
2018_05_21-PM-00_31_44
Last ObjectModification:
2017_10_18-PM-06_50_26
Theory : int_2
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