Nuprl Lemma : imax-list-eq-implies
∀L:ℤ List. ∀a:ℤ. ((a ∈ L)) supposing ((imax-list(L) = a ∈ ℤ) and 0 < ||L||)
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
member-less_than,
length_wf,
subtype_base_sq,
int_subtype_base,
imax-list-member,
equal_wf,
imax-list_wf,
less_than_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
intEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
rename,
axiomEquality,
instantiate,
cumulativity,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}L:\mBbbZ{} List. \mforall{}a:\mBbbZ{}. ((a \mmember{} L)) supposing ((imax-list(L) = a) and 0 < ||L||)
Date html generated:
2016_05_14-PM-01_42_21
Last ObjectModification:
2015_12_26-PM-05_30_36
Theory : list_1
Home
Index