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Proof step 887 from proof bitsand-cast (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 888:
# bits1 = n + # bits0 ∧ # bits0 ≤ # bits1, # bits0 < # bits1, bits0.first ⊦ bits0 = [], bits2 + bits1 = [], bits1 = [], lastn(# bits1, mklist(true, n) + bits0) = lastn(# bits1, fillsgn(# bits1, bits2 + mklist(true, n) + bits0)), false ∈ bits1

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# bits1, # bits0, n] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # bits1, # bits0, n