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Proof step 8 from proof shiftzero-by-one (previous step)

i < ~1, i < 0 ⊦ n = 0, bits2int(firstn(# fillsgn(n, int2bits(i)), false ' + fillsgn(n, int2bits(i)))) = bits2uint(fillsgn(n - 1, int2bits((i - 1) / 2)))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
n = m + 1, i < ~1, i < 0 ⊦ n = 0, bits2int(firstn(# fillsgn(n, int2bits(i)), false ' + fillsgn(n, int2bits(i)))) = bits2uint(fillsgn(m, int2bits((i - 1) / 2)))

Rule argument

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

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m