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Proof step 46 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, i→n(i0) ≤ (i→n(i0) - # int2bits(j)) + # int2bits(j) ⊦ 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(restn((i→n(i0) - # int2bits(j)) + # int2bits(j) - 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 ≤ m ⊦ (m - n) + n = m subst: [n, m] → [# int2bits(j), i→n(i0)] rotate: F spec: nat inst: name: prop-01

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ m +1 = m + 1;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 1 < i → abs(i) = i;% ⊦ 0 < j → abs(j) = j;% ⊦ i < j → ¬ j < i; Used terms: # int2bits(j), i→n(i0)