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Proof step 11 from proof cast-mod-neg-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < ~1 → (# int2bits(i) < m ↔ 0 ≤ i + 2 ^ (n→i(m) - 2)) subst: [m, i] → [i→n(i), j] rotate: F spec: int2bits inst: name: int2bits-lslen-03

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i + j < j ↔ i < 0; Used terms: i→n(i), j