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Proof step 65 from proof int2bytes-rec-pos (previous step)

# uint2bits(i % 256) = 9, uint2bits(i) = uint2bits(i / 256) + uint2bits(i % 256).rest, 128 < i, 127 < i, 1 < i, 0 < i, 127 < i % 256, i % 256 ≤ 255, 255 < i, 0 ≤ i, 0 < i % 256, i % 256 < i ⊦ i % 256 = bits2int(uint2bits(i % 256).rest) + 256, i2b(bits2int(uint2bits(i % 256).rest)) = i2b(i % 256 - 256)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → bits2int(uint2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1) subst: [i] → [i % 256] rotate: F spec: int2bits inst: name: uint2int-rest

Additional information

Used simplifier rules: ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i2b(i) ≠ i2b(j) → i ≠ j; (forward)% ⊦ i + (j - i) = j; Used terms: i % 256