Nuprl Lemma : mu-ge_wf
∀[n:ℤ]. ∀[f:{n...} ⟶ 𝔹]. mu-ge(f;n) ∈ {n...} supposing ∃m:{n...}. (↑(f m))
Proof
Definitions occuring in Statement :
mu-ge: mu-ge(f;n),
int_upper: {i...},
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],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
bool: 𝔹,
uimplies: b supposing a,
top: Top,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bfalse: ff,
false: False
Lemmas referenced :
mu-ge_wf2,
subtype_rel_union,
unit_wf2,
top_wf,
assert_wf,
isl_wf,
int_upper_wf,
bool_wf,
exists_wf,
equal_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionExtensionality,
applyEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
functionEquality,
intEquality,
lambdaFormation,
unionElimination,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[f:\{n...\} {}\mrightarrow{} \mBbbB{}]. mu-ge(f;n) \mmember{} \{n...\} supposing \mexists{}m:\{n...\}. (\muparrow{}(f m))
Date html generated:
2017_04_14-AM-09_18_11
Last ObjectModification:
2017_02_27-PM-03_54_12
Theory : int_2
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