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Proof step 37 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 39:
# bits1 ≠ # bitsand(bits1, bits), # bits = # bits1, # bits1 ≤ # bitsand(bits2, bits3) + # bitsand(bits1, bits) ⊦ bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits1 = [], bits3 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = lastn(# bits1, bitsand(bits2, bits3) + bitsand(bits1, bits))
Proof step 42:
# bits1 = # bitsand(bits1, bits), # bits = # bits1, # bits1 ≤ # bitsand(bits2, bits3) + # bitsand(bits1, bits) ⊦ bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits1 = [], bits3 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = bitsand(bits1, bits)

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [bitsand(bits1, bits), bitsand(bits2, bits3), # bits1] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used terms: bitsand(bits1, bits), bitsand(bits2, bits3), # bits1