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Proof step 1012 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1013:
⊦ ¬ true ∈ bits ∧ (# bits0 < # bits ∧ ¬ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = mklist(false, # bits0)
Proof step 1014:
¬(¬ true ∈ bits1 ∧ # bits0 < # bits1 ∧ ¬ bits0.first ∧ bits1 ≠ [] ∧ bits0 ≠ []), mklist(false, # bits1) = bits1, # bits0 ≤ # bits1 ⊦ bits0 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))), bits2 + bits1 = [], bits1 = [], bits0.first
Proof step 1024:
¬ true ∈ bits1 ∧ # bits0 < # bits1 ∧ ¬ bits0.first ∧ bits1 ≠ [] ∧ bits0 ≠ [], mklist(false, # bits1) = bits1, # bits0 ≤ # bits1 ⊦ bits0 = [], bits1 = lastn(# bits1, fillsgn(# bits1, mklist(false, # bits0))), bits2 + bits1 = [], bits1 = [], bits0.first

Rule argument

name: bitsand-zeros-01 rotate: F subst: [bits0, bits] → [bits0, bits1]

Additional information

Used terms: bits0, bits1