Nuprl - Proof: length less 2 1 1 1

(13steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc

At: length less 2 1 1 1

1. T: Type
2. A: T List
3. B: T List
4. no_repeats(T;A)
5. x:T. (x A) (x B)
6. x: T
7. (x A)
8. i:
9. i < ||B||
10. x = B[i]
11. f: k:||A||j:||B||A[k] = B[j] & j = i
12. k: ||A||

if 1of(f(k)) < i 1of(f(k)) else 1of(f(k))-1 fi (||B||-1)

By: GenConclAtAddr [2;1;1;1] THEN Analyze -2 THEN Reduce 0

Generated subgoal:

1 13. j: ||B||
14. z1: A[k] = B[j] & j = i
15. f(k) = < j,z1 > j:||B||A[k] = B[j] & j = i
if j < i j else j-1 fi (||B||-1) 1 step

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(13steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc