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Proof step 18 from proof bits2bits-def (previous step)

0 < bits2uint((false ' + bitsinvert(bits0))+1) ⊦ sgn(sgn(true ' + bitsinvert((false ' + bitsinvert(bits0))+1)) +1) = sgn(true ' + bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ ¬ false ∈ bits0 → (bits + bits0)+1 = bits +1 + bitsinvert(bits0) subst: [bits0, bits] → [bitsinvert(bits0), false '] rotate: F spec: bitopsaux inst: name: succ-zeros-01

Additional information

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