Nuprl Lemma : ni-eventually-equal_wf
∀[f,g:ℕ∞]. (ni-eventually-equal(f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
ni-eventually-equal: ni-eventually-equal(f;g),
nat-inf: ℕ∞,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
nat-inf: ℕ∞,
uall: ∀[x:A]. B[x],
member: t ∈ T,
ni-eventually-equal: ni-eventually-equal(f;g),
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q
Lemmas referenced :
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
assert_wf,
nat_wf,
set_wf,
int_upper_subtype_nat,
bool_wf,
equal_wf,
int_upper_wf,
all_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
lambdaEquality,
hypothesisEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
dependent_set_memberEquality,
addEquality,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[f,g:\mBbbN{}\minfty{}]. (ni-eventually-equal(f;g) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-01_48_52
Last ObjectModification:
2016_01_15-PM-11_15_40
Theory : basic
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