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Proof step 13 from proof int2bits-len-neg (previous step)

uint2bits(~ j) = false ' + true ' + bits, j + 1 < 2 ^ i, j < i, 0 < 2 ^ i, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, j + 2 ^ i < 0, j + 2 ^ i < i, j < ~1, j < 0, j < 2 ^ i ⊦ bits = [], 1 + # bits = i→n(i + 2), true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
0 ≤ i, 0 ≤ j ⊦ i→n(i) + i→n(j) = i→n(i + j)
Proof step 15:
0 ≤ i ∧ 0 ≤ 2, uint2bits(~ j) = false ' + true ' + bits, j + 1 < 2 ^ i, j < i, 0 < 2 ^ i, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, j + 2 ^ i < 0, j + 2 ^ i < i, j < ~1, j < 0, j < 2 ^ i ⊦ bits = [], 1 + # bits = i→n(i) + i→n(2), true ∈ bits

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) + i→n(j) = i→n(i + j) subst: [j, i] → [2, i] rotate: T spec: intnat inst: name: add

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2, i