Nuprl Lemma : apply_alist_cons_lemma
∀x,v,u,eq:Top. (apply-alist(eq;[u / v];x) ~ if eqof(eq) (fst(u)) x then inl (snd(u)) else apply-alist(eq;v;x) fi )
Proof
Definitions occuring in Statement :
apply-alist: apply-alist(eq;L;x),
cons: [a / b],
eqof: eqof(d),
ifthenelse: if b then t else f fi ,
top: Top,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
apply: f a,
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
apply-alist: apply-alist(eq;L;x),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
eqof: eqof(d)
Lemmas referenced :
top_wf,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}x,v,u,eq:Top.
(apply-alist(eq;[u / v];x) \msim{} if eqof(eq) (fst(u)) x
then inl (snd(u))
else apply-alist(eq;v;x)
fi )
Date html generated:
2016_05_14-AM-06_47_08
Last ObjectModification:
2015_12_26-PM-00_25_03
Theory : list_0
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