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Proof step 34 from proof bitsand-cast-01 (previous step)

# bits = # bits1, # bitsand(bits2, bits3) + # bitsand(bits1, bits) < # bits1 ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits3) + bitsand(bits1, bits))), bits3 = [], bits1 = [], bits3 + bits = [], bits2 = [], bits2 + bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ ¬ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits0

Rule argument

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

Additional information

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