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Proof step 62 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 64:
# bits1 ≠ # bitsand(bits, bits1), # bits1 = # bitsand(bits1, bits), # bits = # bits1 ⊦ bits1 = [], bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits3 = [], lastn(# bits1, bitsand(bits, bits1)) = bitsand(bits1, bits), bits1.first
Proof step 67:
# bits1 = # bitsand(bits, bits1), # bits1 = # bitsand(bits1, bits), # bits = # bits1 ⊦ bits1 = [], bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits3 = [], bitsand(bits, bits1) = bitsand(bits1, bits), bits1.first

Rule argument

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

Additional information

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