Nuprl Lemma : int-to-real_wf
∀[n:ℤ]. (r(n) ∈ ℝ)
Proof
Definitions occuring in Statement :
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
prop: ℙ,
top: Top,
absval: |i|,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
and: P ∧ Q,
subtract: n - m
Lemmas referenced :
zero-mul,
mul-distributes-right,
add-commutes,
mul-associates,
mul-commutes,
mul-swap,
minus-one-mul,
mul-distributes,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermMultiply_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties,
regular-int-seq_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
multiplyEquality,
natural_numberEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
lemma_by_obid,
hypothesis,
lambdaFormation,
isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
minusEquality,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[n:\mBbbZ{}]. (r(n) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-06_47_57
Last ObjectModification:
2016_01_17-AM-01_45_15
Theory : reals
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