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Proof step 601 from proof bitsand-cast (previous step)

sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + 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))), ¬ 2 + # bits + m < # bitsand(bits1, false ' + true ' + bits) ∧ bitsand(bits1, false ' + true ' + bits) ≠ []

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 ' + bits, bits1]

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ (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 ↔ n ≤ m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ ¬ n < n;% ⊦ n < # bits → lastn(n, fillsgn(n, bits)) = lastn(n, bits);% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → ¬ n < m; Used terms: false ' + true ' + bits, bits1