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Proof step 10 from proof uint2uint-inv (previous step)

2 ^ n→i(# uint2bits(i / 2)) = bits2uint(bitsinvert(uint2bits(i / 2))) + i / 2 + 1, 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → 2 ^ n→i(# uint2bits(i0)) = bits2uint(bitsinvert(uint2bits(i0))) + i0 + 1 ⊦ i = 1, (bits2uint(bitsinvert(uint2bits(i / 2))) + i / 2 + 1) * 2 = 1 + bits2uint(bitsinvert(uint2bits(i / 2)) + (i % 2 ≠ 1)') + i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bits2uint-rec-02 rotate: F subst: [boolvar, bits] → [i % 2 ≠ 1, bitsinvert(uint2bits(i / 2))]

Additional information

Used simplifier rules: bits2uint-zero: ⊦ bits2uint(bits + false ') = bits2uint(bits) * 2;% ⊦ i % 2 ≠ 1 ∧ 0 < i → i / 2 * 2 = i;% ⊦ i * j + i = i * (j + 1);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ i % 2 = 1 → (1 + i / 2) * 2 = i + 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j = i + i0 ↔ j = i0; Used terms: i % 2 ≠ 1, bitsinvert(uint2bits(i / 2))