Nuprl Lemma : qmin-list_wf
∀[L:ℚ List]. qmin-list(L) ∈ ℚ supposing 0 < ||L||
Proof
Definitions occuring in Statement :
qmin-list: qmin-list(L),
rationals: ℚ,
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
qmin-list: qmin-list(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
combine-list_wf,
rationals_wf,
qmin_wf,
less_than_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[L:\mBbbQ{} List]. qmin-list(L) \mmember{} \mBbbQ{} supposing 0 < ||L||
Date html generated:
2016_05_15-PM-10_43_17
Last ObjectModification:
2015_12_27-PM-07_56_14
Theory : rationals
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