Nuprl Lemma : mu_wf
∀[f:ℕ ⟶ 𝔹]. mu(f) ∈ ℕ supposing ∃n:ℕ. (↑(f n))
Proof
Definitions occuring in Statement :
mu: mu(f),
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mu: mu(f),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_upper: {i...},
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
mu-ge_wf,
subtype_rel_dep_function,
nat_wf,
bool_wf,
int_upper_wf,
subtype_rel_self,
assert_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
because_Cache,
lambdaFormation,
productElimination,
dependent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. mu(f) \mmember{} \mBbbN{} supposing \mexists{}n:\mBbbN{}. (\muparrow{}(f n))
Date html generated:
2016_05_14-AM-07_29_30
Last ObjectModification:
2015_12_26-PM-01_26_27
Theory : int_2
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