Nuprl Lemma : strictness-ifthenelse
∀[a,b:Top]. (if ⊥ then a else b fi ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ifthenelse: if b then t else f fi ,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
strictness-decide,
bottom-sqle,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
sqequalAxiom,
hypothesisEquality
Latex:
\mforall{}[a,b:Top]. (if \mbot{} then a else b fi \msim{} \mbot{})
Date html generated:
2016_05_15-PM-02_07_26
Last ObjectModification:
2015_12_27-AM-00_37_25
Theory : untyped!computation
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