Nuprl Lemma : list-max_wf
∀[T:Type]. ∀[f:T ⟶ ℤ]. ∀[L:T List]. list-max(x.f[x];L) ∈ i:ℤ × {x:T| f[x] = i ∈ ℤ} supposing 0 < ||L||
Proof
Definitions occuring in Statement :
list-max: list-max(x.f[x];L),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
list-max: list-max(x.f[x];L),
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
and: P ∧ Q
Lemmas referenced :
outl_wf,
equal-wf-T-base,
top_wf,
list-max-aux_wf,
list-max-aux-property,
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,
productEquality,
intEquality,
setEquality,
cumulativity,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List]. list-max(x.f[x];L) \mmember{} i:\mBbbZ{} \mtimes{} \{x:T| f[x] = i\} supposing 0 < ||L|\000C|
Date html generated:
2016_05_14-PM-01_43_07
Last ObjectModification:
2015_12_26-PM-05_31_36
Theory : list_1
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