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Proof step 40 from proof int2bits-neg-03 (previous step)

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

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))) +1 + false '] rotate: F spec: bitopsaux inst: name: sgn-one-01

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ ¬ bits +1 ≠ [] ↔ false;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ bits + boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ ¬ true ∈ bits +1 ↔ false; Used terms: boolvar, bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) +1 + false '