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Proof step 19 from proof int2bits-rec-neg (previous step)

i < 0 ⊦ sgn(bitsinvert(uint2bits(~ i)) + true ') = sgn(bitsinvert(uint2bits(1 - i)) +1) + true ', i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 ≤ j → uint2bits(j) = sgn(bitsinvert(bitsinvert(uint2bits(j + 1)) +1))
Proof step 21:
0 ≤ ~ i, i < 0 ⊦ sgn(bitsinvert(sgn(bitsinvert(bitsinvert(uint2bits(~ i + 1)) +1))) + true ') = sgn(bitsinvert(uint2bits(1 - i)) +1) + true ', i = 0

Rule argument

name: uint2bits-succ-intro rotate: F subst: [j] → [~ i]

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: ~ i