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Proof step 28 from proof bits2bits-def (previous step)

0 < bits2uint(false ' + bitsinvert(bits) + true ' + bits1) ⊦ bits1 = [], sgn(sgn(true ' + bits + false ' + bitsinvert(bits1)) +1) = sgn(true ' + bits + true ' + bits1), true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ true ∈ bits → sgn(bits + false ' + bits0) = sgn(bits) + false ' + bits0 subst: [bits0, bits] → [bitsinvert(bits1), true ' + bits] rotate: F spec: bitopsaux inst: name: sgn-append-02

Additional information

Used simplifier rules: ⊦ ¬ boolvar ∈ boolvar0 ' + bits ↔ ¬(boolvar ↔ boolvar0) ∧ ¬ boolvar ∈ bits;% ⊦ ¬ true ∈ bits → sgn(bits + false ' + bits0) = sgn(false ' + bits0);% ⊦ (bits + false ' + bits0)+1 = bits + (false ' + bits0)+1;% ⊦ ¬ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits +1 + bits0;% ⊦ false ' +1 = true ';% ⊦ sgn(sgn(bits) + bits0) = sgn(bits + bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bitsinvert(bits1), true ' + bits