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Proof step 102 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 103:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 104:
¬(# bits = #(true ' + false ' + bits1) ∧ bits2 ≠ [] ∧ mklist(true, n0 - 1) ≠ [] ∧ bits ≠ []), # bits = 2 + # bits1, sgn(mklist(true, n0 - 1) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, n0 - 1) + true ' + false ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2 + bits, mklist(true, n0 - 1) + true ' + false ' + bits1))), n0 = 0, bits2 + bits = []
Proof step 109:
# bits = #(true ' + false ' + bits1) ∧ bits2 ≠ [] ∧ mklist(true, n0 - 1) ≠ [] ∧ bits ≠ [], # bits = 2 + # bits1, sgn(mklist(true, n0 - 1) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, n0 - 1) + true ' + false ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2, mklist(true, n0 - 1)) + bitsand(bits, true ' + false ' + bits1))), n0 = 0, bits2 + bits = []

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [true ' + false ' + bits1, mklist(true, n0 - 1), bits, bits2]

Additional information

Used terms: true ' + false ' + bits1, mklist(true, n0 - 1), bits, bits2