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Proof step 495 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bitsand(bits2, bits4) + # bitsand(bits1, true ' + false ' + bits) < # bits1 ⊦ bits4 + bits1 = [], bits1 = [], lastn(# bits1, fillsgn(# bits1, bits4 + bitsand(bits1, true ' + false ' + bits))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, true ' + false ' + bits))), bits2 = [], bits4 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 496:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits

Rule argument

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

Additional information

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