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Proof step 204 from proof bitsand-cast (previous step)

n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, 2 + # bits1 + m < # bitsand(mklist(false, m), bits2) + # bitsand(bits, false ' + true ' + bits1), 2 + # bits1 + m < n, n < # bitsand(mklist(false, m), bits2) + # bitsand(bits, false ' + true ' + bits1), 3 + # bits1 + m < # bitsand(mklist(false, m), bits2) + # bitsand(bits, false ' + true ' + bits1) ⊦ fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], m = 0, bits = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → ¬ n < m; Used terms: false ' + true ' + bits1, bits