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Proof step 738 from proof bitsand-cast (previous step)

2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bitsand(false ' + true ' + bits, bits1) < # bits1 ⊦ bits4 + bits0 = [], bits0 = [], bits1 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, mklist(false, # bits0) + bitsand(false ' + true ' + bits, bits1))), bits4 = [], (bits4 + bits0) + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 739:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)

Rule argument

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

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n → ¬ n < m; Used terms: bits1, false ' + true ' + bits