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Proof step 13 from proof cast-band (previous step)

⊦ bits2int(bitsand(int2bits(bits2int([])), false ')) = bits2int(bitsand(int2bits(j), false '))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '
Proof step 15:
int2bits(j) ≠ [] ∧ false ' = false ' ⊦ bits2int(bitsand(int2bits(bits2int([])), false ')) = bits2int(false ')

Rule argument

name: and-rec-02 rotate: F subst: [bits0, bits] → [false ', int2bits(j)]

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: false ', int2bits(j)