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Proof step 49 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits

Rule argument

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

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false);% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m + n = n + m;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m +1 = m + 1;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m + n < m; Used terms: bits1, bits3 + bits