Nuprl Lemma : imax-list_functionality
∀[L,L':ℤ List]. (imax-list(L) = imax-list(L') ∈ ℤ) supposing (set-equal(ℤ;L;L') and 0 < ||L||)
Proof
Definitions occuring in Statement :
set-equal: set-equal(T;x;y),
imax-list: imax-list(L),
length: ||as||,
list: T List,
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 :
prop: ℙ,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x],
l_subset: l_subset(T;as;bs),
set-equal: set-equal(T;x;y),
true: True,
subtype_rel: A ⊆r B,
subtract: n - m,
uiff: uiff(P;Q),
not: ¬A,
decidable: Dec(P),
le: A ≤ B,
nat: ℕ,
rev_implies: P ⇐ Q,
top: Top,
cons: [a / b],
false: False,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
or: P ∨ Q,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j ,
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b
Lemmas referenced :
list_wf,
length_wf,
less_than_wf,
set-equal_wf,
imax-list-subset,
l_member_wf,
equal_wf,
le-add-cancel,
add-zero,
add-associates,
add_functionality_wrt_le,
add-commutes,
minus-one-mul-top,
zero-add,
minus-one-mul,
minus-add,
condition-implies-le,
not-lt-2,
false_wf,
decidable__lt,
nat_wf,
length_wf_nat,
nil_member,
cons_member,
length_of_cons_lemma,
product_subtype_list,
length_of_nil_lemma,
list-cases,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
non_neg_length,
decidable__le,
hd_wf,
btrue_neq_bfalse,
nil_wf,
member-implies-null-eq-bfalse,
btrue_wf,
null_cons_lemma,
null_nil_lemma,
hd_member,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int
Rules used in proof :
natural_numberEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
axiomEquality,
isect_memberEquality,
sqequalRule,
intEquality,
hypothesis,
independent_isectElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
productElimination,
dependent_functionElimination,
lambdaFormation,
minusEquality,
lambdaEquality,
applyEquality,
independent_pairFormation,
addEquality,
rename,
setElimination,
inlFormation,
voidEquality,
hypothesis_subsumption,
promote_hyp,
voidElimination,
imageElimination,
unionElimination,
int_eqEquality,
dependent_pairFormation,
approximateComputation
Latex:
\mforall{}[L,L':\mBbbZ{} List]. (imax-list(L) = imax-list(L')) supposing (set-equal(\mBbbZ{};L;L') and 0 < ||L||)
Date html generated:
2017_09_29-PM-05_57_52
Last ObjectModification:
2017_07_31-PM-02_07_47
Theory : list_1
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