Nuprl Lemma : ml-gcd-list-sq
∀[L:ℤ List+]. (ml-gcd-list(L) ~ gcd-list(L))
Proof
Definitions occuring in Statement :
ml-gcd-list: ml-gcd-list(L),
gcd-list: gcd-list(L),
listp: A List+,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
gcd-list: gcd-list(L),
ml-gcd-list: ml-gcd-list(L),
and: P ∧ Q,
cand: A c∧ B,
listp: A List+,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
cons: [a / b],
top: Top,
implies: P ⇒ Q,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
prop: ℙ,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
true: True,
sq_type: SQType(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
listp_wf,
int-valueall-type,
ml-gcd_wf,
tl_wf,
hd_wf,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__le,
false_wf,
not-ge-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
equal_wf,
subtype_base_sq,
int_subtype_base,
better-gcd_wf,
ml-gcd-sq,
ml-accumulate-sq,
eager-accum-list_accum,
list_accum_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
natural_numberEquality,
sqequalAxiom,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
independent_pairFormation,
lambdaEquality,
hypothesisEquality,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
sqequalRule,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
lambdaFormation,
addEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
applyEquality,
minusEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
cumulativity
Latex:
\mforall{}[L:\mBbbZ{} List\msupplus{}]. (ml-gcd-list(L) \msim{} gcd-list(L))
Date html generated:
2017_09_29-PM-05_51_35
Last ObjectModification:
2017_05_21-PM-04_28_00
Theory : ML
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