Nuprl Lemma : length-shadow-vec
∀[as,bs:ℤ List]. ∀[i:ℕ||as||]. ||shadow-vec(i;as;bs)|| = (||as|| - 1) ∈ ℤ 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],
subtract: n - m,
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),
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
has-value: (a)↓,
guard: {T},
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True
Lemmas referenced :
evalall-reduce,
int-vec-mul_wf,
select_wf,
sq_stable__le,
list-valueall-type,
int-valueall-type,
value-type-has-value,
list_wf,
list-value-type,
less_than_transitivity1,
length_wf,
le_weakening,
int-vec-add_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
int_seg_wf,
list-delete_wf,
equal_wf,
squash_wf,
true_wf,
length-list-delete,
int_seg_subtype_nat,
false_wf,
less_than_wf,
length-int-vec-mul,
length-int-vec-add,
iff_weakening_equal,
subtract_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
intEquality,
hypothesisEquality,
setElimination,
rename,
hypothesis,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
callbyvalueReduce,
minusEquality,
dependent_functionElimination,
baseApply,
closedConclusion,
applyEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
universeEquality,
independent_pairFormation,
lambdaFormation,
voidElimination,
voidEquality
Latex:
\mforall{}[as,bs:\mBbbZ{} List]. \mforall{}[i:\mBbbN{}||as||]. ||shadow-vec(i;as;bs)|| = (||as|| - 1) supposing ||as|| = ||bs||
Date html generated:
2017_04_14-AM-08_56_14
Last ObjectModification:
2017_02_27-PM-03_39_47
Theory : omega
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