Nuprl Lemma : mul-list-merge
∀[ns2,ns1:ℤ List]. (Π(merge-int(ns1;ns2)) = (Π(ns1) * Π(ns2) ) ∈ ℤ)
Proof
Definitions occuring in Statement :
mul-list: Π(ns) ,
merge-int: merge-int(as;bs),
list: T List,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
merge-int: merge-int(as;bs),
all: ∀x:A. B[x],
top: Top,
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,
mul-list: Π(ns)
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
reduce_nil_lemma,
mul_list_nil_lemma,
decidable__equal_int,
mul-list_wf,
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,
reduce_cons_lemma,
equal_wf,
squash_wf,
true_wf,
mul-list-insert-int,
merge-int_wf,
subtype_rel_self,
cons_wf,
iff_weakening_equal,
mul-swap
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
hypothesis,
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,
lambdaFormation,
rename,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
multiplyEquality,
imageMemberEquality,
productElimination,
axiomEquality
Latex:
\mforall{}[ns2,ns1:\mBbbZ{} List]. (\mPi{}(merge-int(ns1;ns2)) = (\mPi{}(ns1) * \mPi{}(ns2) ))
Date html generated:
2018_05_21-PM-06_57_32
Last ObjectModification:
2017_07_26-PM-04_59_49
Theory : general
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