Nuprl Lemma : qmul-mul
∀[x,y:ℤ]. (x * y ~ x * y)
Proof
Definitions occuring in Statement :
qmul: r * s,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qmul: r * s,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
valueall-type-has-valueall,
int-valueall-type,
evalall-reduce
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
callbyvalueReduce,
because_Cache,
isintReduceTrue,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[x,y:\mBbbZ{}]. (x * y \msim{} x * y)
Date html generated:
2016_05_15-PM-10_37_49
Last ObjectModification:
2015_12_27-PM-08_00_00
Theory : rationals
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