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Proof step 652 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bits1 < # bitsand(false ' + true ' + bits, bits1), # bits1 ≤ # bits2 + # bitsand(false ' + true ' + bits, bits1), # bits3 ≤ m, bits3.first ⊦ m = 0, bits3 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, mklist(false, m) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], # bits1 = # bitsand(false ' + true ' + bits, bits1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 653:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 654:
false ' + true ' + bits ≠ [] ∧ bits1 ≠ [], # bits1 = 2 + # bits, # bits1 < # bitsand(bits1, false ' + true ' + bits), # bits1 ≤ # bits2 + # bitsand(bits1, false ' + true ' + bits), # bits3 ≤ m, bits3.first ⊦ m = 0, bits3 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits)), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], # bits1 = # bitsand(bits1, false ' + true ' + bits)

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits1, false ' + true ' + bits]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits1, false ' + true ' + bits