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Proof step 182 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 183:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1)

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [false ' + true ' + bits1, bits, bits2]

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;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ m +1 = m + 1;% ⊦ m < n → ¬ n < m; Used terms: false ' + true ' + bits1, bits, bits2