Nuprl Lemma : cons-nat-seq_wf
∀[n:ℕ]. ∀[a:ℕ ⟶ ℕ]. (cons-nat-seq(n;a) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
cons-nat-seq: cons-nat-seq(n;a),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
prop: ℙ,
and: P ∧ Q,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
cons-nat-seq: cons-nat-seq(n;a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
le_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
subtract_wf,
nat_wf
Rules used in proof :
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
dependent_pairFormation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
isectElimination,
dependent_set_memberEquality,
extract_by_obid,
functionExtensionality,
applyEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
because_Cache,
rename,
thin,
setElimination,
sqequalHypSubstitution,
int_eqEquality,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (cons-nat-seq(n;a) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2017_04_20-AM-07_35_26
Last ObjectModification:
2017_04_07-PM-05_52_41
Theory : continuity
Home
Index