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Proof step 77 from proof cast-help-comm (previous step)

i→n(i) ≤ # int2bits(j), i < i0, 0 < i, 0 < i0, 1 < i0, i ≤ i0, i→n(i0) ≤ (i→n(i0) - i→n(i)) + i→n(i) ⊦ i0 = 0, i = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(restn((i→n(i0) - i→n(i)) + i→n(i) - i→n(i0), mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
n ≤ m ⊦ (m - n) + n = m
Proof step 79:
i→n(i) ≤ i→n(i0), i→n(i) ≤ # int2bits(j), i < i0, 0 < i, 0 < i0, 1 < i0, i ≤ i0, i→n(i0) ≤ i→n(i0) ⊦ i0 = 0, i = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(restn(i→n(i0) - i→n(i0), mklist(lastn(i→n(i), int2bits(j)).first, i→n(i0) - i→n(i)) + lastn(i→n(i), int2bits(j))))

Rule argument

seq: n ≤ m ⊦ (m - n) + n = m subst: [n, m] → [i→n(i), i→n(i0)] rotate: F spec: nat inst: name: prop-01

Additional information

Used simplifier rules: ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ 1 < i → abs(i) = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: i→n(i), i→n(i0)