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Proof step 57 from proof bitsand-cast-04 (previous step)

# bits0 ≤ n, # bits0 = 1 + # bits1, # bits1 < n, # bits1 < # bits0, n ≤ # bits2 + # bits0, # bits1 < # bits2 + # bits0, # bits0 ≤ n ⊦ sgn(bitsand(lastn(n - # bits0, bits2) + bits0, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], bits0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
n = n0 + # bits0, # bits0 ≤ n, # bits0 = 1 + # bits1, # bits1 < n, # bits1 < # bits0, n ≤ # bits2 + # bits0, # bits1 < # bits2 + # bits0, # bits0 ≤ n ⊦ sgn(bitsand(lastn(n0, bits2) + bits0, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], bits0 = []

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bits0, n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits0, n0