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Proof step 66 from proof cast-mod-neg-low (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ i < ~1 → (# int2bits(i) ≤ m ↔ 0 ≤ i + 2 ^ (n→i(m) - 1))
Proof step 68:
¬ j % 2 ^ i < ~1, i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0, 0 < i, # int2bits(j % 2 ^ i) ≤ i→n(i) ⊦ bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest) = j % 2 ^ i + 2 ^ i, j = ~1, i = 1, j % 2 ^ i = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i→n(i), j % 2 ^ i