Nuprl Lemma : rmaximum-shift
∀[k,n,m:ℤ]. ∀[x:Top]. rmaximum(n;m;i.x[i]) ~ rmaximum(n - k;m - k;i.x[i + k]) supposing n ≤ m
Proof
Definitions occuring in Statement :
rmaximum: rmaximum(n;m;k.x[k]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
le: A ≤ B,
subtract: n - m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
rmaximum: rmaximum(n;m;k.x[k]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
and: P ∧ Q,
ge: i ≥ j ,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
intformand_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
le_wf,
nat_wf,
nat_properties,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
less_than_wf,
subtract_wf,
equal_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtract-add-cancel,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
itermAdd_wf,
int_term_value_add_lemma,
top_wf,
primrec-unroll
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
sqequalAxiom,
equalityElimination,
productElimination,
promote_hyp,
isect_memberFormation
Latex:
\mforall{}[k,n,m:\mBbbZ{}]. \mforall{}[x:Top]. rmaximum(n;m;i.x[i]) \msim{} rmaximum(n - k;m - k;i.x[i + k]) supposing n \mleq{} m
Date html generated:
2017_10_03-AM-09_02_46
Last ObjectModification:
2017_07_28-AM-07_40_24
Theory : reals
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