Nuprl Lemma : mul-list-bag-product
∀L:ℤ List. (Π(L) = Π(L) ∈ ℤ)
Proof
Definitions occuring in Statement :
mul-list: Π(ns) ,
int-bag-product: Π(b),
list: T List,
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
int-bag-product: Π(b),
mul-list: Π(ns) ,
bag-product: Πx ∈ b. f[x],
bag-summation: Σ(x∈b). f[x],
bag-accum: bag-accum(v,x.f[v; x];init;bs),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
list_induction,
all_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
list_accum_nil_lemma,
reduce_nil_lemma,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermMultiply_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
list_accum_cons_lemma,
reduce_cons_lemma,
equal_wf,
squash_wf,
true_wf,
reduce_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
lambdaEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
computeAll,
rename,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
multiplyEquality,
imageMemberEquality,
productElimination
Latex:
\mforall{}L:\mBbbZ{} List. (\mPi{}(L) = \mPi{}(L))
Date html generated:
2018_05_21-PM-06_57_39
Last ObjectModification:
2017_07_26-PM-04_59_55
Theory : general
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