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Proof step 98 from proof cast-mod-neg-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 99:
⊦ i + 1 ≠ 0 → (~1 ≤ i ↔ 0 ≤ i)
Proof step 100:
¬ j % 2 ^ i + 1 ≠ 0, i→n(i) = # int2bits(j % 2 ^ i).rest, i→n(i) < # int2bits(j % 2 ^ i), j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < j % 2 ^ i, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < 0, 0 < i, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, ~1 ≤ j % 2 ^ i ⊦ bits2int(int2bits(j % 2 ^ i).rest) = j % 2 ^ i, j = ~1, i = 1, j % 2 ^ i = 0
Proof step 103:
j % 2 ^ i + 1 ≠ 0, i→n(i) = # int2bits(j % 2 ^ i).rest, i→n(i) < # int2bits(j % 2 ^ i), j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < j % 2 ^ i, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < 0, 0 < i, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, 0 ≤ j % 2 ^ i ⊦ bits2int(int2bits(j % 2 ^ i).rest) = j % 2 ^ i, j = ~1, i = 1, j % 2 ^ i = 0

Rule argument

seq: ⊦ i + 1 ≠ 0 → (~1 ≤ i ↔ 0 ≤ i) subst: [i] → [j % 2 ^ i] rotate: F spec: int-abs inst: name: mone-07

Additional information

Used terms: j % 2 ^ i