Nuprl Lemma : select-le-imax-list
∀L:ℤ List. ∀i:ℕ||L||. (L[i] ≤ imax-list(L))
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_exists: (∃x∈L. P[x])
Lemmas referenced :
imax-list-ub,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
independent_isectElimination,
setElimination,
rename,
productElimination,
hypothesis,
imageElimination,
unionElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
intEquality
Latex:
\mforall{}L:\mBbbZ{} List. \mforall{}i:\mBbbN{}||L||. (L[i] \mleq{} imax-list(L))
Date html generated:
2019_10_15-AM-10_21_27
Last ObjectModification:
2019_06_26-PM-01_48_42
Theory : list_1
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