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Proof step 46 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ ¬ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits0
Proof step 48:
¬(¬ bits1.first ∧ # bits1 ≤ #(bits3 + bits) ∧ bits1 ≠ []), # bits1 = # bitsand(bits1, bits), # bits = # bits1, # bitsand(bits3 + bits, bits1) < # bits1 ⊦ bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits1 = [], bits3 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = bitsand(bits1, bits)

Rule argument

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

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ n < n; Used terms: bits1, bits3 + bits