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Proof step 24 from proof cast-mod-pos-high (previous step)

# int2bits(j) = i→n(i) + 1, 0 ≤ i, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, j < 2 ^ i ⊦ j % 2 ^ i = bits2int(int2bits(j).rest) + 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1) subst: [i] → [j] rotate: F spec: int2bits inst: name: int2int-rest

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ int2bits(0) = false ';% ⊦ # boolvar ' = 0 +1;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;%j ≠ 0 ⊦ 0 % j = 0;% ⊦ boolvar '.rest = [];% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 0 ≤ i → (i < 1 ↔ i = 0);% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; Used terms: j