Nuprl Lemma : mu-ge_wf2
∀[n:ℤ]. ∀[f:{n...} ⟶ (Top + Top)]. mu-ge(f;n) ∈ {n...} supposing ∃m:{n...}. (↑isl(f m))
Proof
Definitions occuring in Statement :
mu-ge: mu-ge(f;n),
int_upper: {i...},
assert: ↑b,
isl: isl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
exists: ∃x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
mu-ge: mu-ge(f;n),
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
isl: isl(x),
assert: ↑b,
btrue: tt,
bfalse: ff,
has-value: (a)↓
Lemmas referenced :
exists_wf,
int_upper_wf,
assert_wf,
isl_wf,
top_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
le_wf,
subtract_wf,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
nat_wf,
subtype_base_sq,
int_subtype_base,
int_upper_properties,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
true_wf,
false_wf,
equal_wf,
value-type-has-value,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
isect_memberEquality,
because_Cache,
functionEquality,
unionEquality,
intEquality,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
unionElimination,
instantiate,
cumulativity,
dependent_set_memberEquality,
callbyvalueReduce,
applyLambdaEquality
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[f:\{n...\} {}\mrightarrow{} (Top + Top)]. mu-ge(f;n) \mmember{} \{n...\} supposing \mexists{}m:\{n...\}. (\muparrow{}isl(f m))
Date html generated:
2017_04_14-AM-09_18_07
Last ObjectModification:
2017_02_27-PM-03_54_24
Theory : int_2
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