Nuprl Lemma : regular-int-seq-weakening
∀[n,k:ℤ]. ∀[f:ℕ+ ⟶ ℤ]. (k-regular-seq(f)) supposing (n-regular-seq(f) and (n ≤ k))
Proof
Definitions occuring in Statement :
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
nat: ℕ,
nat_plus: ℕ+,
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,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
subtype_rel: A ⊆r B
Lemmas referenced :
mul_preserves_le,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMultiply_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
nat_plus_wf,
less_than'_wf,
absval_wf,
subtract_wf,
nat_wf,
regular-int-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
dependent_set_memberEquality,
multiplyEquality,
natural_numberEquality,
addEquality,
setElimination,
rename,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
productElimination,
because_Cache,
independent_pairEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[n,k:\mBbbZ{}]. \mforall{}[f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. (k-regular-seq(f)) supposing (n-regular-seq(f) and (n \mleq{} k))
Date html generated:
2017_10_02-PM-07_12_56
Last ObjectModification:
2017_07_05-PM-03_38_43
Theory : reals
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