Nuprl Lemma : select-upto
∀[m:ℕ]. ∀[n:ℕm]. (upto(m)[n] ~ n)
Proof
Definitions occuring in Statement :
upto: upto(n),
select: L[n],
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
select_upto,
int_seg_wf,
nat_wf,
int_subtype_base
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
sqequalIntensionalEquality,
applyEquality,
sqequalRule,
equalityTransitivity
Latex:
\mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m]. (upto(m)[n] \msim{} n)
Date html generated:
2016_10_21-AM-10_14_32
Last ObjectModification:
2016_07_12-AM-05_31_13
Theory : list_1
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