Nuprl Lemma : shadow-vec_wf
∀[as,bs:ℤ List]. ∀[i:ℕ||as||]. shadow-vec(i;as;bs) ∈ ℤ List supposing ||as|| = ||bs|| ∈ ℤ
Proof
Definitions occuring in Statement :
shadow-vec: shadow-vec(i;as;bs),
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
shadow-vec: shadow-vec(i;as;bs),
has-value: (a)↓,
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
list-delete_wf,
int-vec-add_wf,
int_seg_wf,
equal_wf,
le_weakening,
length_wf,
less_than_transitivity1,
list-value-type,
list_wf,
value-type-has-value,
int-valueall-type,
list-valueall-type,
sq_stable__le,
select_wf,
int-vec-mul_wf,
evalall-reduce
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
intEquality,
hypothesisEquality,
setElimination,
rename,
hypothesis,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
minusEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[as,bs:\mBbbZ{} List]. \mforall{}[i:\mBbbN{}||as||]. shadow-vec(i;as;bs) \mmember{} \mBbbZ{} List supposing ||as|| = ||bs||
Date html generated:
2016_05_14-AM-06_57_26
Last ObjectModification:
2016_01_14-PM-08_43_54
Theory : omega
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