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Proof step 10 from proof cast-help-comm (previous step)

i < i0, 0 < i, 0 < i0, 1 < i0 ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(bits2int(lastn(i→n(i0), fillsgn(i→n(i0), int2bits(j)))))))) = bits2int(lastn(i→n(i0), fillsgn(i→n(i0), int2bits(bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits) subst: [bits] → [lastn(i→n(i0), fillsgn(i→n(i0), int2bits(j)))] rotate: F spec: int2bits inst: name: bits2bits-def

Additional information

Used simplifier rules: ⊦ lastn(n, bits) = [] ↔ n = 0;% ⊦ i→n(i) = 0 ↔ i = 0;%bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits);% ⊦ fillsgn(0, bits) = bits;% ⊦ lastn(0, bits) = []; Used terms: lastn(i→n(i0), fillsgn(i→n(i0), int2bits(j)))