Nuprl Lemma : increasing-sequence_wf
∀[a:ℕ ⟶ ℕ]. (increasing-sequence(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
increasing-sequence: increasing-sequence(a),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
uiff: uiff(P;Q),
guard: {T},
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
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 ,
nat: ℕ,
so_lambda: λ2x.t[x],
increasing-sequence: increasing-sequence(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_formula_prop_eq_lemma,
intformeq_wf,
add-is-int-iff,
false_wf,
add_nat_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,
equal_wf,
or_wf,
nat_wf,
all_wf
Rules used in proof :
functionEquality,
axiomEquality,
independent_functionElimination,
productElimination,
baseClosed,
closedConclusion,
baseApply,
promote_hyp,
pointwiseFunctionality,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
lambdaFormation,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
natural_numberEquality,
rename,
setElimination,
addEquality,
dependent_set_memberEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
because_Cache,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (increasing-sequence(a) \mmember{} \mBbbP{})
Date html generated:
2017_04_20-AM-07_36_30
Last ObjectModification:
2017_04_15-PM-05_03_38
Theory : continuity
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