Nuprl Lemma : record-select-update
∀[r,x,y,v:Top]. (r[x := v].y ~ if y =a x then v else r.y fi )
Proof
Definitions occuring in Statement :
record-update: r[x := v],
record-select: r.x,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rec_select_update_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[r,x,y,v:Top]. (r[x := v].y \msim{} if y =a x then v else r.y fi )
Date html generated:
2016_05_15-PM-06_42_53
Last ObjectModification:
2015_12_27-AM-11_50_09
Theory : general
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