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Proof step 400 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, (bits2 + mklist(true, n - 1)) + true ' + false ' + bits))), n = 0, bits3 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 401:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 402:
¬(# bits1 = #(true ' + false ' + bits) ∧ bits3 ≠ [] ∧ bits2 + mklist(true, n - 1) ≠ [] ∧ bits1 ≠ []), # bits1 = 2 + # bits, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, (bits2 + mklist(true, n - 1)) + true ' + false ' + bits))), n = 0, bits3 + bits1 = []
Proof step 405:
# bits1 = #(true ' + false ' + bits) ∧ bits3 ≠ [] ∧ bits2 + mklist(true, n - 1) ≠ [] ∧ bits1 ≠ [], # bits1 = 2 + # bits, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3, bits2 + mklist(true, n - 1)) + bitsand(bits1, true ' + false ' + bits))), n = 0, bits3 + bits1 = []

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [true ' + false ' + bits, bits2 + mklist(true, n - 1), bits1, bits3]

Additional information

Used terms: true ' + false ' + bits, bits2 + mklist(true, n - 1), bits1, bits3