Nuprl Lemma : imin_unfold
∀[a,b:ℤ]. (imin(a;b) = if a ≤z b then a else b fi ∈ ℤ)
Proof
Definitions occuring in Statement :
imin: imin(a;b),
le_int: i ≤z j,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
imin: imin(a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
uimplies: b supposing a
Lemmas referenced :
value-type-has-value,
int-value-type,
ifthenelse_wf,
le_int_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. (imin(a;b) = if a \mleq{}z b then a else b fi )
Date html generated:
2016_05_14-AM-07_21_26
Last ObjectModification:
2015_12_26-PM-01_31_35
Theory : int_2
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