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Proof step 4 from proof band-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

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