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Proof step 4 from proof band-notneg-01 (previous step)

0 ≤ j, bits2int(bitsand(int2bits(i), int2bits(j))) < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ bits ≠ [] → (bits2int(bits) < 0 ↔ bits.first)
Proof step 6:
bitsand(int2bits(i), int2bits(j)) ≠ [], 0 ≤ j, bitsand(int2bits(i), int2bits(j)).first ⊦

Rule argument

seq: ⊦ bits ≠ [] → (bits2int(bits) < 0 ↔ bits.first) subst: [bits] → [bitsand(int2bits(i), int2bits(j))] rotate: F spec: int2bits inst: name: bits2int-lez

Additional information

Used simplifier rules: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ []; Used terms: bitsand(int2bits(i), int2bits(j))