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Proof step 8 from proof int2bytes-rec-pos-04 (previous step)

0 < i, 0 < i % 256, 255 < i, 128 ≤ i % 256, 0 ≤ i, 256 ≤ i ⊦ int2bytes(i % 256).rest = fix(2, int2bytes(i % 256)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i % 256]

Additional information

Used simplifier rules: fix-two-01: ⊦ fix(2, by ' + by0 ') = by ' + by0 ';% ⊦ ¬ 255 < i % 256;% ⊦ ¬ i ≤ j ↔ j < i;%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j;% ⊦ (by ' + bytes).rest = bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by ' = by0 ' ↔ by = by0; Used terms: i % 256