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Proof step 41 from proof int2bits-len-neg (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 43:
0 ≤ i, 0 = 2 ^ (i + 1) + 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 + 1)).rest.rest, 2 ^ i + j < 0 ⊦ # uint2bits(2 ^ (i + 1)) = i→n(i + 2)

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i, 2] rotate: T spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: i, 2