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Proof step 394 from proof bitsand-cast (previous step)

sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(true, n - 1)) + true ' + false ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 395:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 396:
#(true ' + false ' + bits) ≤ # bits1 ∧ true ' + false ' + bits ≠ [] ∧ (true ' + false ' + bits).first, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(true, n - 1)) + true ' + false ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []

Rule argument

name: bitsand-app-true rotate: F subst: [bits1, bits0, bits] → [true ' + false ' + bits, bits1, bits3]

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (boolvar ' + bits).first ↔ 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: true ' + false ' + bits, bits1, bits3