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Proof step 39 from proof int2bits-len-neg (previous step)

0 = 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j + 2 ^ i < 0, j < 0, j + 1 < 2 ^ i, j < i, j + 2 ^ i < i, j < ~1, j < 2 ^ i, true ∈ uint2bits(2 ^ i * 2).rest.rest, 2 ^ i + j < 0 ⊦ # uint2bits(2 ^ i * 2) = i→n(i + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ i * j = j * i
Proof step 41:
0 = 2 * 2 ^ i + j, 0 ≤ i, 0 < 2 ^ i, j + 2 ^ i < 0, j < 0, j + 1 < 2 ^ i, j < i, j + 2 ^ i < i, j < ~1, j < 2 ^ i, true ∈ uint2bits(2 * 2 ^ i).rest.rest, 2 ^ i + j < 0 ⊦ # uint2bits(2 * 2 ^ i) = i→n(i + 2)

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [2, 2 ^ i] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used terms: 2, 2 ^ i