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Proof step 4 from proof int2int-neg (previous step)

j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦ j = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
0 ≤ j ⊦ j < 2 ^ (n→i(# int2bits(j)) - 1)
Proof step 6:
~ j < 2 ^ (n→i(# int2bits(~ j)) - 1), j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦ j = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

Rule argument

name: int2bits-less-2pot subst: [j] → [~ j]

Additional information

Used simplifier rules: ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: ~ j