Nuprl Lemma : remove-repeats-normal-form
∀[eq,L:Top].
(rec-case(L) of
[] => []
a::_ =>
r.[a / rec-case(r) of [] => [] | a@0::_ => r.if eq a@0 a then r else [a@0 / r] fi ] ~ remove-repeats(eq;L))
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
list_ind: list_ind,
cons: [a / b],
nil: [],
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,
list_ind: list_ind,
cons: [a / b],
ifthenelse: if b then t else f fi ,
nil: [],
it: ⋅,
remove-repeats: remove-repeats(eq;L),
filter: filter(P;l),
reduce: reduce(f;k;as),
bnot: ¬bb,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
bfalse: ff,
btrue: tt
Latex:
\mforall{}[eq,L:Top].
(rec-case(L) of
[] => []
a::$_{}$ =>
r.[a / rec-case(r) of [] => [] | a@0::$_{}$ => r.if eq a@0 a then r else [a@\000C0 / r] fi ]
\msim{} remove-repeats(eq;L))
Date html generated:
2016_05_16-AM-11_02_17
Last ObjectModification:
2016_01_17-PM-03_47_33
Theory : event-ordering
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