Nuprl Lemma : lookup_cons_pr_lemma
∀cs,b,a,k,z,s:Top. ([<a, b> / cs][k] ~ if a (=b) k then b else cs[k] fi )
Proof
Definitions occuring in Statement :
lookup: as[k],
cons: [a / b],
ifthenelse: if b then t else f fi ,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
pair: <a, b>,
sqequal: s ~ t,
set_eq: =b
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
lookup: as[k],
ycomb: Y,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
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{}cs,b,a,k,z,s:Top. ([<a, b> / cs][k] \msim{} if a (=\msubb{}) k then b else cs[k] fi )
Date html generated:
2016_05_16-AM-08_16_43
Last ObjectModification:
2015_12_28-PM-06_27_36
Theory : polynom_2
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