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Proof step 231 from proof bitsand-cast (previous step)

2 + # bits1 = # bits, sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), n0 + # bits = # fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n0 + # bits ⊦ bits = [], m = 0, bits2 = [], bits2 + bits = [], mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 232:
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits
Proof step 233:
¬(¬ true ∈ mklist(false, m) ∧ (# mklist(false, m) ≤ # bits2 ∨ bits2.first) ∧ mklist(false, m) ≠ [] ∧ bits2 ≠ []), 2 + # bits1 = # bits, sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), n0 + # bits = # fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n0 + # bits ⊦ bits = [], m = 0, bits2 = [], bits2 + bits = [], mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))
Proof step 253:
¬ true ∈ mklist(false, m) ∧ (# mklist(false, m) ≤ # bits2 ∨ bits2.first) ∧ mklist(false, m) ≠ [] ∧ bits2 ≠ [], 2 + # bits1 = # bits, sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n0 + # bits ⊦ bits = [], m = 0, bits2 = [], bits2 + bits = [], mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, mklist(false, m) + bitsand(bits, false ' + true ' + bits1))

Rule argument

name: bitsand-zeros rotate: F subst: [bits0, bits] → [bits2, mklist(false, m)]

Additional information

Used terms: bits2, mklist(false, m)