Nuprl Lemma : imax-list-append2
∀[as,bs:ℤ List]. (imax-list(as @ bs) = imax(imax-list(as);imax-list(bs)) ∈ ℤ) supposing (0 < ||bs|| and 0 < ||as||)
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
length: ||as||,
append: as @ bs,
list: T List,
imax: imax(a;b),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
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,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
imax-list: imax-list(L),
combine-list: combine-list(x,y.f[x; y];L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b],
nat_plus: ℕ+,
uiff: uiff(P;Q)
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
less_than_wf,
length_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
length_of_nil_lemma,
list_ind_nil_lemma,
length_of_cons_lemma,
list_ind_cons_lemma,
decidable__lt,
append_wf,
length-append,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
imax-list_wf,
equal_wf,
imax_wf,
iff_weakening_equal,
imax_assoc,
squash_wf,
true_wf,
imax-list-cons,
list-cases,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
list_accum_nil_lemma,
product_subtype_list,
list_accum_cons_lemma,
add_nat_plus,
length_wf_nat,
nat_plus_wf,
nat_plus_properties,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
hypothesis,
natural_numberEquality,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
addEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
imageMemberEquality,
universeEquality,
promote_hyp,
hypothesis_subsumption,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination,
pointwiseFunctionality
Latex:
\mforall{}[as,bs:\mBbbZ{} List].
(imax-list(as @ bs) = imax(imax-list(as);imax-list(bs))) supposing (0 < ||bs|| and 0 < ||as||)
Date html generated:
2017_04_17-AM-07_39_49
Last ObjectModification:
2017_02_27-PM-04_13_02
Theory : list_1
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