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Proof step 901 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 902:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ ¬ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits0
Proof step 903:
¬(¬ false ∈ bits1 ∧ # bits0 ≤ # bits1 ∧ ¬ bits0.first ∧ bits0 ≠ []), mklist(true, # bits1) = bits1, # bits0 < # bits1 ⊦ bits2 + bits1 = [], bits0 = [], bits1 = [], lastn(# bits1, mklist(false, # bits1 - # bits0) + bits0) = lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))), bits0.first

Rule argument

name: add-ones-grlen-02 rotate: F subst: [bits0, bits] → [bits0, bits1]

Additional information

Used simplifier rules: ⊦ ¬ false ∈ bits → mklist(true, # bits) = bits;%⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits; Used terms: bits0, bits1