Nuprl Lemma : gcd-list_wf
∀[L:ℤ List+]. (gcd-list(L) ∈ ℤ)
Proof
Definitions occuring in Statement :
gcd-list: gcd-list(L),
listp: A List+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
gcd-list: gcd-list(L),
uimplies: b supposing a,
all: ∀x:A. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
eager-accum_wf,
tl_wf,
hd_wf,
decidable__le,
length_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
better-gcd_wf,
int-valueall-type,
listp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
sqequalRule,
lemma_by_obid,
isectElimination,
intEquality,
because_Cache,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_pairFormation,
lambdaFormation,
voidElimination,
productElimination,
independent_functionElimination,
addEquality,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidEquality,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L:\mBbbZ{} List\msupplus{}]. (gcd-list(L) \mmember{} \mBbbZ{})
Date html generated:
2016_05_14-AM-06_56_59
Last ObjectModification:
2015_12_26-PM-01_14_14
Theory : omega
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