Step
*
1
2
1
1
of Lemma
firstn_decomp2
.....equality.....
1. T : Type
2. j : ℤ
3. 0 < j
4. ∀[l:T List]. (firstn(j - 1 - 1;l) @ [l[j - 1 - 1]] ~ firstn(j - 1;l)) supposing (((j - 1) ≤ ||l||) and 0 < j - 1)
5. l : T List
6. 0 < j
7. j ≤ ||l||
8. ¬(j = 1 ∈ ℤ)
9. firstn(j - 1 - 1;tl(l)) @ [tl(l)[j - 1 - 1]] ~ firstn(j - 1;tl(l))
⊢ l ~ [hd(l) / tl(l)]
BY
{ (BackThruLemma `list_decomp` THEN Auto) }
Latex:
Latex:
.....equality.....
1. T : Type
2. j : \mBbbZ{}
3. 0 < j
4. \mforall{}[l:T List]
(firstn(j - 1 - 1;l) @ [l[j - 1 - 1]] \msim{} firstn(j - 1;l)) supposing
(((j - 1) \mleq{} ||l||) and
0 < j - 1)
5. l : T List
6. 0 < j
7. j \mleq{} ||l||
8. \mneg{}(j = 1)
9. firstn(j - 1 - 1;tl(l)) @ [tl(l)[j - 1 - 1]] \msim{} firstn(j - 1;tl(l))
\mvdash{} l \msim{} [hd(l) / tl(l)]
By
Latex:
(BackThruLemma `list\_decomp` THEN Auto)
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