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Proof step 34 from proof int2bits-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
0 ≤ i, 2 ^ i ≤ j, j < 2 ^ (i + 1) ⊦ # uint2bits(j) = i→n(i + 2)
Proof step 36:
¬(0 ≤ i ∧ 2 ^ i ≤ ~ j ∧ ~ j < 2 ^ (i + 1)), true ∈ uint2bits(~ j).rest.rest, j < 2 ^ i, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i, j < 0 ⊦ # uint2bits(~ j) = i→n(i + 2)

Rule argument

name: uint2bits-len rotate: F subst: [i, j] → [i, ~ j]

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: i, ~ j