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Proof step 6 from proof cast-law-and-one (previous step)

0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), sgn(bitsand(int2bits(j), int2bits(j0)))))) = cast(i, band(cast(i, j), j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ bits ≠ [] → lastn(n, fillsgn(n, sgn(bits))) = lastn(n, fillsgn(n, bits))
Proof step 8:
bitsand(int2bits(j), int2bits(j0)) ≠ [], 0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = cast(i, band(cast(i, j), j0))

Rule argument

seq: ⊦ bits ≠ [] → lastn(n, fillsgn(n, sgn(bits))) = lastn(n, fillsgn(n, bits)) subst: [bits, n] → [bitsand(int2bits(j), int2bits(j0)), i→n(i)] rotate: F spec: bitopsaux inst: name: lastn-fill-sgn

Additional information

Used simplifier rules: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ []; Used terms: bitsand(int2bits(j), int2bits(j0)), i→n(i)