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Proof step 19 from proof uint2bits-2pot-02 (previous step)

0 < i1, 1 < 2 ^ (i1 + 1), ~1 ≤ i1, 0 < 2 ^ (i1 + 1), 0 ≤ 2 ^ (i1 + 1), ∀ i0. i→n(i0) < i→n(i1 + 1) → 0 < i0 → uint2bits(2 ^ i0 - 1) = false ' + mklist(true, i→n(i0)) ⊦ 0 = i1, uint2bits(2 ^ i1 - 1) + true ' = false ' + true ' + mklist(true, i→n(i1))

User applied rule apply induction

And closed the goal!

Rule argument

subst: [i0] → [i1]

Additional information

Used simplifier rules: ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ ¬ i < i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i1