Nuprl Lemma : real-regular
∀[x:ℝ]. ∀[k:ℕ+]. k-regular-seq(x)
Proof
Definitions occuring in Statement :
real: ℝ,
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
real: ℝ,
uimplies: b supposing a,
all: ∀x:A. B[x],
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,
regular-int-seq: k-regular-seq(f),
le: A ≤ B,
subtype_rel: A ⊆r B,
nat: ℕ,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
sq_stable: SqStable(P)
Lemmas referenced :
regular-int-seq-weakening,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_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_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
less_than'_wf,
absval_wf,
subtract_wf,
nat_wf,
nat_plus_wf,
real_wf,
sq_stable__regular-int-seq,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
productElimination,
independent_pairEquality,
because_Cache,
multiplyEquality,
addEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[k:\mBbbN{}\msupplus{}]. k-regular-seq(x)
Date html generated:
2017_10_02-PM-07_13_11
Last ObjectModification:
2017_07_05-PM-03_42_23
Theory : reals
Home
Index