Nuprl Lemma : mk-finite-nat-seq_wf
∀[n:ℕ]. ∀[f:ℕn ⟶ ℕ]. (f^(n) ∈ finite-nat-seq())
Proof
Definitions occuring in Statement :
mk-finite-nat-seq: f^(n),
finite-nat-seq: finite-nat-seq(),
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,
mk-finite-nat-seq: f^(n),
finite-nat-seq: finite-nat-seq(),
nat: ℕ
Lemmas referenced :
nat_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_pairEquality,
hypothesisEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}]. (f\^{}(n) \mmember{} finite-nat-seq())
Date html generated:
2016_05_14-PM-09_54_32
Last ObjectModification:
2016_01_15-AM-07_44_28
Theory : continuity
Home
Index