Nuprl Lemma : imax-list-unique
∀[L:ℤ List]. ∀[a:ℤ]. uiff(imax-list(L) = a ∈ ℤ;(∀b∈L.b ≤ a)) supposing (a ∈ L)
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
list: T List,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
cons: [a / b],
top: Top,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
guard: {T},
decidable: Dec(P),
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_all: (∀x∈L.P[x]),
le: A ≤ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
imax-list-lb,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
product_subtype_list,
length_of_cons_lemma,
add_nat_plus,
length_wf_nat,
less_than_wf,
nat_plus_wf,
nat_plus_properties,
decidable__lt,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
equal_wf,
imax-list-ub,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
less_than'_wf,
int_seg_wf,
length_wf,
equal-wf-base,
int_subtype_base,
l_all_wf,
le_wf,
l_member_wf,
select_wf,
int_seg_properties,
list_subtype_base,
list_wf,
l_exists_iff,
le_weakening,
decidable__equal_int
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
intEquality,
dependent_functionElimination,
unionElimination,
sqequalRule,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
lambdaFormation,
applyLambdaEquality,
setElimination,
rename,
pointwiseFunctionality,
baseApply,
closedConclusion,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
computeAll,
independent_pairEquality,
because_Cache,
axiomEquality,
applyEquality,
setEquality,
imageElimination,
productEquality
Latex:
\mforall{}[L:\mBbbZ{} List]. \mforall{}[a:\mBbbZ{}]. uiff(imax-list(L) = a;(\mforall{}b\mmember{}L.b \mleq{} a)) supposing (a \mmember{} L)
Date html generated:
2017_04_14-AM-09_23_57
Last ObjectModification:
2017_02_27-PM-03_58_52
Theory : list_1
Home
Index