Nuprl - Proof: length less 2 1 2

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

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

Inj(||A||; (||B||-1); k.if 1of(f(k)) < i 1of(f(k)) else 1of(f(k))-1 fi)

By: Unfold `inject` 0 THEN Reduce 0 THEN RepeatFor 2 (Analyze 0) THEN GenConclAtAddr [1;2;1;1;1] THEN Thin -1 THEN Analyze -1 THEN Reduce 0 THEN GenConclAtAddr [1;3;1;1;1] THEN Thin -1 THEN Analyze -1 THEN Reduce 0

Generated subgoal:

1 12. a1: ||A||
13. a2: ||A||
14. j: ||B||
15. z1: A[a1] = B[j] & j = i
16. j1: ||B||
17. z2: A[a2] = B[j1] & j1 = i
if j < i j else j-1 fi = if j1 < i j1 else j1-1 fi (||B||-1) a1 = a2 1 step

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