Nuprl Lemma : mk-rational-qdiv
∀[a,b:ℤ]. (mk-rational(a;b) ~ (a/b))
Proof
Definitions occuring in Statement :
qdiv: (r/s),
mk-rational: mk-rational(a;b),
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qdiv: (r/s),
mk-rational: mk-rational(a;b),
qinv: 1/r,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
ifthenelse: if b then t else f fi ,
btrue: tt,
qmul: r * s,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
bfalse: ff
Lemmas referenced :
valueall-type-has-valueall,
int-valueall-type,
evalall-reduce,
product-valueall-type,
mul-one
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,
productEquality,
lambdaEquality,
independent_functionElimination,
lambdaFormation,
independent_pairEquality,
natural_numberEquality,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. (mk-rational(a;b) \msim{} (a/b))
Date html generated:
2016_05_15-PM-10_39_21
Last ObjectModification:
2015_12_27-PM-07_59_12
Theory : rationals
Home
Index