Nuprl Lemma : ni-iterated-min_wf
∀[n:ℕ]. ∀[f:ℕn ⟶ ℕ∞]. (ni-iterated-min(n;f) ∈ ℕ∞)
Proof
Definitions occuring in Statement :
ni-iterated-min: ni-iterated-min(n;f),
nat-inf: ℕ∞,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ni-iterated-min: ni-iterated-min(n;f),
nat: ℕ
Lemmas referenced :
primrec_wf,
nat-inf_wf,
nat-inf-infinity_wf,
ni-min_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}\minfty{}]. (ni-iterated-min(n;f) \mmember{} \mBbbN{}\minfty{})
Date html generated:
2016_05_15-PM-01_48_47
Last ObjectModification:
2015_12_27-AM-00_08_50
Theory : basic
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