Nuprl Lemma : remove1_cons_lemma
∀bs,b,a,s:Top. ([b / bs] \ a ~ if b (=b) a then bs else [b / (bs \ a)] fi )
Proof
Definitions occuring in Statement :
remove1: as \ a,
cons: [a / b],
ifthenelse: if b then t else f fi ,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
sqequal: s ~ t,
set_eq: =b
Definitions unfolded in proof :
all: ∀x:A. B[x],
remove1: as \ a,
ycomb: Y,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}bs,b,a,s:Top. ([b / bs] \mbackslash{} a \msim{} if b (=\msubb{}) a then bs else [b / (bs \mbackslash{} a)] fi )
Date html generated:
2016_05_16-AM-07_38_53
Last ObjectModification:
2015_12_28-PM-05_44_07
Theory : list_2
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