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Proof step 13 from proof bib-pos-high (previous step)

0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 64 ≤ i ⊦ i % 256 = b2i(i2b(bits2int(lastn(8, int2bits(i))))) + 256, 0 = i, lastn(8, int2bits(i)).first

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i, 256, i0, j] rotate: T spec: int-div inst: name: div-elim-pos

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j); (elim) Used terms: i, 256, i0, j