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Proof step 5 from proof int2bits-len-neg (previous step)

j < 2 ^ i, j < 0, 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 ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 < j, true ∈ uint2bits(j).rest.rest ⊦ sgn(bitsinvert(uint2bits(j)) +1) = bitsinvert(uint2bits(j)) +1
Proof step 7:
¬(0 < ~ j ∧ true ∈ uint2bits(~ j).rest.rest), j < 2 ^ i, j < 0, 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 ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2)
Proof step 30:
0 < ~ j ∧ true ∈ uint2bits(~ j).rest.rest, j < 2 ^ i, j < 0, 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 ⊦ # bitsinvert(uint2bits(~ j)) +1 = i→n(i + 2)

Rule argument

name: uint2bits-sgn-2pot-01 rotate: F subst: [j] → [~ j]

Additional information

Used terms: ~ j