Nuprl Lemma : no_repeats_upto
∀[n:ℕ]. (no_repeats(ℤ;upto(n)) ∧ no_repeats(ℕn;upto(n)))
Proof
Definitions occuring in Statement :
upto: upto(n),
no_repeats: no_repeats(T;l),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
upto: upto(n),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
implies: P ⇒ Q
Lemmas referenced :
no_repeats_from-upto,
no_repeats-subtype,
int_seg_wf,
upto_wf,
no_repeats_witness,
subtype_rel_list,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_pairFormation,
intEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
productElimination,
independent_pairEquality,
applyEquality,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}]. (no\_repeats(\mBbbZ{};upto(n)) \mwedge{} no\_repeats(\mBbbN{}n;upto(n)))
Date html generated:
2016_05_14-PM-02_05_05
Last ObjectModification:
2015_12_26-PM-05_09_14
Theory : list_1
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