Nuprl Lemma : ni-selector_wf
∀[p:ℕ∞ ⟶ 𝔹]. (ni-selector(p) ∈ ℕ∞)
Proof
Definitions occuring in Statement :
ni-selector: ni-selector(p),
nat-inf: ℕ∞,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ni-selector: ni-selector(p),
nat-inf: ℕ∞,
nat: ℕ,
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,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_apply: x[s],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
bool_wf,
nat-inf_wf,
all_wf,
assert_wf,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
assert-b-exists,
assert_of_bnot,
nat_wf,
int_seg_wf,
false_wf,
int_seg_subtype_nat,
nat2inf_wf,
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,
b-exists_wf,
bnot_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
lambdaFormation,
because_Cache,
productElimination,
independent_functionElimination,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:\mBbbN{}\minfty{} {}\mrightarrow{} \mBbbB{}]. (ni-selector(p) \mmember{} \mBbbN{}\minfty{})
Date html generated:
2016_05_15-PM-01_47_14
Last ObjectModification:
2016_01_15-PM-11_17_22
Theory : basic
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