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Proof step 42 from proof int2bits-neg-03 (previous step)

0 ≤ 2 ^ n→i(# int2bits(~ j)) + j, uint2bits(2 ^ n→i(# int2bits(~ j)) + j) = boolvar ', j < 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
uint2bits(2 ^ n→i(# int2bits(~ j)) + j) = boolvar ', j < 2 ^ n→i(# int2bits(~ j)), 0 < 2 ^ n→i(# int2bits(~ j)), 0 ≤ 2 ^ n→i(# int2bits(~ j)) + j, j < 0, j + 1 < 2 ^ n→i(# int2bits(~ j)) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i +1 = i + 1;% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < i + j ↔ 0 < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)