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Proof step 185 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 186:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 187:
false ' + true ' + bits1 ≠ [] ∧ bits ≠ [], n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, n0 - 1), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], n0 - 1 = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # [] = 0;% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; Used terms: bits, false ' + true ' + bits1