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Proof step 43 from proof bitsand-cast-01 (previous step)

# bits = # bits1, # bits1 = # bitsand(bits1, bits) ⊦ 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 44:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 45:
¬ # bits1 ≤ # bitsand(bits3 + bits, bits1), # bits = # bits1, # bits1 = # bitsand(bits1, bits) ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = bitsand(bits1, bits), bits3 = [], bits1 = [], bits3 + bits = [], bits2 = [], bits2 + bits1 = []
Proof step 51:
# bits1 ≤ # bitsand(bits3 + bits, bits1), # bits = # bits1, # bits1 = # bitsand(bits1, bits) ⊦ lastn(# bits1, bitsand(bits3 + bits, bits1)) = bitsand(bits1, bits), bits3 = [], bits1 = [], bits3 + bits = [], bits2 = [], bits2 + bits1 = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bitsand(bits3 + bits, bits1), # bits1] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: bitsand(bits3 + bits, bits1), # bits1