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Proof step 756 from proof bitsand-cast (previous step)

2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 757:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 758:
¬ # bits1 ≤ # bitsand(false ' + true ' + bits, bits1), 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(false ' + true ' + bits, bits1))
Proof step 767:
# bits1 ≤ # bitsand(false ' + true ' + bits, bits1), 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(false ' + true ' + bits, bits1))

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [bitsand(false ' + true ' + bits, bits1), bitsand(bits2, bits4), # bits1] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used terms: bitsand(false ' + true ' + bits, bits1), bitsand(bits2, bits4), # bits1