Nuprl Lemma : qavg_wf
∀[a,b:ℚ]. (qavg(a;b) ∈ ℚ)
Proof
Definitions occuring in Statement :
qavg: qavg(a;b),
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
qavg: qavg(a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
qeq: qeq(r;s),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
btrue: tt,
eq_int: (i =z j),
bfalse: ff,
assert: ↑b,
false: False,
prop: ℙ
Lemmas referenced :
qdiv_wf,
qadd_wf,
assert-qeq,
equal_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
voidElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbQ{}]. (qavg(a;b) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_05_59
Last ObjectModification:
2015_12_27-PM-07_45_25
Theory : rationals
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