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Proof step 610 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 611:
⊦ bits ≠ [] ∧ bits0 ≠ [] → (bitsand(bits, bits0).first ↔ bits.first ∧ bits0.first)
Proof step 612:
bits1 ≠ [] ∧ false ' + true ' + bits ≠ [], sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ lastn(2 + # bits + m, mklist(bits1.first ∧ (false ' + true ' + bits).first, m) + bitsand(bits1, false ' + true ' + bits)) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1))), bitsand(bits1, false ' + true ' + bits) = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = []

Rule argument

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

Additional information

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