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Proof step 78 from proof bitsand-cast-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 79:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 80:
# bits1 ≠ # bitsand(bits1, true ' + bits), # bits1 ≤ # bitsand(bits1, true ' + bits), # bits < # bits1, # bits < # bitsand(bits1, true ' + bits) ⊦ lastn(# bits1, bitsand(bits1, true ' + bits)) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, true ' + bits))), bits2 + bits1 = [], bits2 = [], bits1 = []
Proof step 83:
# bits1 = # bitsand(bits1, true ' + bits), # bits1 ≤ # bitsand(bits1, true ' + bits), # bits < # bits1, # bits < # bitsand(bits1, true ' + bits) ⊦ bitsand(bits1, true ' + bits) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, true ' + bits))), bits2 + bits1 = [], bits2 = [], bits1 = []

Rule argument

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

Additional information

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