Nuprl Lemma : length-int-vec-add
∀[as,bs:ℤ List]. ||as + bs|| = ||bs|| ∈ ℤ supposing ||as|| = ||bs|| ∈ ℤ
Proof
Definitions occuring in Statement :
int-vec-add: as + bs,
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
int-vec-add: as + bs,
nil: [],
it: ⋅,
all: ∀x:A. B[x],
top: Top,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
equal-wf-base,
length_of_nil_lemma,
length_of_cons_lemma,
spread_cons_lemma,
int_subtype_base,
list_subtype_base,
length_wf,
int-vec-add_wf,
equal_wf,
squash_wf,
true_wf,
add_functionality_wrt_eq,
iff_weakening_equal,
decidable__equal_int,
false_wf,
not-equal-2,
le_antisymmetry_iff,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
zero-add,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
intEquality,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
independent_functionElimination,
natural_numberEquality,
lambdaFormation,
rename,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
addEquality,
imageElimination,
universeEquality,
imageMemberEquality,
productElimination,
unionElimination,
independent_pairFormation,
minusEquality
Latex:
\mforall{}[as,bs:\mBbbZ{} List]. ||as + bs|| = ||bs|| supposing ||as|| = ||bs||
Date html generated:
2017_04_14-AM-08_55_41
Last ObjectModification:
2017_02_27-PM-03_39_34
Theory : omega
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