Nuprl Lemma : rbinop_wf
∀[op:ℤ]. ∀[p,q:ℝ]. rbinop(op;p;q) ∈ ℝ supposing ((op = 6 ∈ ℤ) ⇒ q ≠ r0) ∧ ((op = 10 ∈ ℤ) ⇒ (r0 < p))
Proof
Definitions occuring in Statement :
rbinop: rbinop(op;p;q),
rneq: x ≠ y,
rless: x < y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rbinop: rbinop(op;p;q),
and: P ∧ Q,
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
rsub_wf,
rmul_wf,
rdiv_wf,
rmax_wf,
rmin_wf,
radd_wf,
realexp_wf,
rless_wf,
int-to-real_wf,
equal-wf-base,
int_subtype_base,
rneq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
int_eqEquality,
hypothesisEquality,
natural_numberEquality,
extract_by_obid,
isectElimination,
hypothesis,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
functionEquality,
intEquality,
applyEquality,
baseClosed,
isect_memberEquality
Latex:
\mforall{}[op:\mBbbZ{}]. \mforall{}[p,q:\mBbbR{}]. rbinop(op;p;q) \mmember{} \mBbbR{} supposing ((op = 6) {}\mRightarrow{} q \mneq{} r0) \mwedge{} ((op = 10) {}\mRightarrow{} (r0 < p))
Date html generated:
2017_10_04-PM-11_01_42
Last ObjectModification:
2017_07_28-AM-08_53_39
Theory : reals_2
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