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Proof step 18 from proof shiftzero-rec-neg-longer (previous step)

i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2), n ≤ # int2bits((i - 1) / 2) + 1 ⊦ i = ~1, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(false, i→n(j)) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)')) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(false, i→n(j) - 1) + int2bits((i - 1) / 2)))

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [i→n(j), m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ firstn(# bits + n, bits + bits0) = bits + firstn(n, bits0);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ firstn(# bits, bits) = bits;% ⊦ bits2int(int2bits(i)) = i;%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: i→n(j), m