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Proof step 7 from proof int2int-neg (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
n→i(# int2bits(~ j)) = i + 1, 2 ^ n→i(# int2bits(~ j)) + j < 2 ^ i, 1 < 2 ^ i, 2 ^ n→i(# int2bits(~ j)) < 2 ^ i, 2 ^ n→i(# int2bits(~ j)) + 1 < 2 ^ i, j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0, 0 < 2 ^ i + j, 0 ≤ 2 ^ i, 0 < 2 ^ i, j + 1 < 2 ^ i, j < 2 ^ i, (2 ^ n→i(# int2bits(~ j)) + j) + 1 < 2 ^ i ⊦ j = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [n→i(# int2bits(~ j)), 1, i] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: n→i(# int2bits(~ j)), 1, i