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Proof step 956 from proof bitsand-cast (previous step)

⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(sgn(bits1), bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 957:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits) = false '
Proof step 958:
¬ true ∈ bits1 ∧ bits1 ≠ [] ⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(false ', bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), true ∈ bits1

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits) = false ' subst: [bits] → [bits1] rotate: F spec: bitopsaux inst: name: sgn-zero

Additional information

Used simplifier rules: ⊦ # [] = 0;% ⊦ sgn([]) = [];% ⊦ fillsgn(0, bits) = bits;% ⊦ lastn(0, bits) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits1