Nuprl Lemma : imax-list-strict-lb
∀[L:ℤ List]. ∀[a:ℤ]. uiff(imax-list(L) < a;(∀b∈L.b < a)) supposing 0 < ||L||
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
l_all: (∀x∈L.P[x]),
length: ||as||,
list: T List,
less_than: a < b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
l_all: (∀x∈L.P[x]),
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list_wf,
l_member_wf,
l_all_wf,
less_than_wf,
member-less_than,
int_seg_wf,
select_wf,
decidable__lt,
length_wf,
int_seg_properties,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
imax-list_wf,
decidable__le,
subtract_wf,
imax-list-lb
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
productElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
lambdaFormation,
setElimination,
rename,
setEquality,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L:\mBbbZ{} List]. \mforall{}[a:\mBbbZ{}]. uiff(imax-list(L) < a;(\mforall{}b\mmember{}L.b < a)) supposing 0 < ||L||
Date html generated:
2016_05_14-PM-01_41_50
Last ObjectModification:
2016_01_15-AM-08_23_50
Theory : list_1
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