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Proof step 879 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 880:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 881:
# bits0 ≤ # bits1 ∧ bits0 ≠ [] ∧ bits0.first, mklist(true, # bits1) = bits1, # bits0 < # bits1, bits0.first ⊦ bits1 = [], lastn(# bits1, fillsgn(# bits1, bits0)) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0))), bits0 = [], bits2 + bits1 = []

Rule argument

name: bitsand-app-true rotate: F subst: [bits1, bits0, bits] → [bits0, bits1, bits2]

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits0, bits1, bits2