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Proof step 762 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(false ' + true ' + bits, bits1), # bitsand(false ' + true ' + bits, bits1) < # bits1 ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 763:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 764:
false ' + true ' + bits ≠ [] ∧ bits1 ≠ [], # bits1 = 2 + # bits, # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(bits1, false ' + true ' + bits), # bitsand(bits1, false ' + true ' + bits) < # bits1 ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + 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