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Proof step 201 from proof bitsand-cast (previous step)

2 + # bits1 = # bits, sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n ⊦ n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], m = 0, bits2 = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 202:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 203:
¬ #(bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)) ≤ n, 2 + # bits1 = # bits, sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n ⊦ n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], m = 0, bits2 = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)))

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [ bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1), n] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1), n