Nuprl Lemma : qinv-elim
∀[r:ℚ]. (1/r ~ if isint(r) then <1, r> else let p,q = r in <q, p> fi )
Proof
Definitions occuring in Statement :
qinv: 1/r,
rationals: ℚ,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
isint: isint def,
spread: spread def,
pair: <a, b>,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qinv: 1/r,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
rationals_wf,
rationals-valueall-type,
evalall-reduce
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
hypothesisEquality,
callbyvalueReduce,
sqequalAxiom
Latex:
\mforall{}[r:\mBbbQ{}]. (1/r \msim{} if isint(r) then ə, r> else let p,q = r in <q, p> fi )
Date html generated:
2016_05_15-PM-10_39_39
Last ObjectModification:
2015_12_27-PM-07_58_55
Theory : rationals
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