Nuprl Lemma : remove-first-cons
∀[L,x,P:Top]. (remove-first(P;[x / L]) ~ if P x then L else [x / remove-first(P;L)] fi )
Proof
Definitions occuring in Statement :
remove-first: remove-first(P;L),
cons: [a / b],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
remove-first: remove-first(P;L),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[L,x,P:Top]. (remove-first(P;[x / L]) \msim{} if P x then L else [x / remove-first(P;L)] fi )
Date html generated:
2016_05_14-PM-02_47_11
Last ObjectModification:
2015_12_26-PM-02_38_16
Theory : list_1
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