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Proof step 17 from proof int2int-rest-01 (previous step)

int2bits(j) = true ' + false ' + bits, 2 ^ (2 + n→i(# bits)) + j = bits2uint(bits) + 2 ^ (1 + n→i(# bits)), j < 0, j < ~1 ⊦ j = 0, bits2uint(bits) = 2 ^ (1 + n→i(# bits)) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [n→i(# bits), 2, 2] rotate: F spec: int-pot inst: name: pot-dist-pos

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n);% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* i2) * i + j = (* i1) * i + j0 ↔ (i2 - i1) * i + j = j0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: n→i(# bits), 2, 2