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Proof step 882 from proof bitsand-cast (previous step)

mklist(true, # bits1) = bits1, # bits0 < # bits1, bits0.first ⊦ bits2 + bits1 = [], bits0 = [], bits1 = [], lastn(# bits1, mklist(true, # bits1 - # bits0) + bits0) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 883:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 884:
¬(¬ false ∈ bits1 ∧ # bits0 ≤ # bits1 ∧ bits0.first ∧ bits0 ≠ []), mklist(true, # bits1) = bits1, # bits0 < # bits1, bits0.first ⊦ bits2 + bits1 = [], bits0 = [], bits1 = [], lastn(# bits1, mklist(true, # bits1 - # bits0) + bits0) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0)))
Proof step 886:
¬ false ∈ bits1 ∧ # bits0 ≤ # bits1 ∧ bits0.first ∧ bits0 ≠ [], mklist(true, # bits1) = bits1, # bits0 < # bits1, bits0.first ⊦ bits2 + bits1 = [], bits0 = [], bits1 = [], lastn(# bits1, mklist(true, # bits1 - # bits0) + bits0) = lastn(# bits1, fillsgn(# bits1, bits2 + fillsgn(# bits1, bits0)))

Rule argument

name: add-ones-grlen rotate: F subst: [bits0, bits] → [bits0, bits1]

Additional information

Used terms: bits0, bits1