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Proof step 57 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ 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: bits1, bits