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Proof step 177 from proof bitsand-cast (previous step)

n = # fillsgn(n, false ' + true ' + bits1), # bits = 2 + # bits1, n0 - 1 = 0, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + bits = [], n0 = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 178:
n0 = m + 1, n = # fillsgn(n, false ' + true ' + bits1), # bits = 2 + # bits1, m = 0, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + bits = [], n0 = 0

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n0, 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: n0, m