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Proof step 36 from proof cast-mod-neg-low (previous step)

0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, i→n(i) ≤ # int2bits(j / 2 ^ i - 1) + # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest)) = j % 2 ^ i + 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 38:
i→n(i) ≠ # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, i→n(i) ≤ # int2bits(j / 2 ^ i - 1) + # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest)) = j % 2 ^ i + 2 ^ i
Proof step 62:
i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, i→n(i) ≤ # int2bits(j / 2 ^ i - 1) + # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest) = j % 2 ^ i + 2 ^ i

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, int2bits(j / 2 ^ i - 1), i→n(i)] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used terms: fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, int2bits(j / 2 ^ i - 1), i→n(i)