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Proof step 43 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0 ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: n ≤ # bits ⊦ lastn(n, bits) = restn(# bits - n, bits) subst: [bits, n] → [mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j), i→n(i0)] rotate: F spec: list-del inst: bitlista name: lastN-restN

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n + (m - n) < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j), i→n(i0)