Nuprl Lemma : less-as-ifthenelse
∀[r,s,x,y:Top]. (if (r) < (s) then x else y ~ if r <z s then x else y fi )
Proof
Definitions occuring in Statement :
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
top: Top,
less: if (a) < (b) then c else d,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
Error :less_as_ite,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r,s,x,y:Top]. (if (r) < (s) then x else y \msim{} if r <z s then x else y fi )
Date html generated:
2018_05_21-PM-00_03_38
Last ObjectModification:
2018_01_28-PM-02_27_40
Theory : bool_1
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