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Proof step 34 from proof int2bits-neg-03 (previous step)

~1 = (2 ^ n→i(# int2bits(~ j)) + j) % 2, sgn(bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) + true ') = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦ ~1 = 2 ^ n→i(# int2bits(~ j)) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → (sgn(bits) = boolvar ' ↔ ¬ (¬ boolvar) ∈ bits) subst: [boolvar, bits] → [boolvar, bitsinvert (uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) + true '] rotate: F spec: bitopsaux inst: name: sgn-one-01

Additional information

Used simplifier rules: uint2bits-empty: 0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: boolvar, bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) + true '