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Proof step 1036 from proof bitsand-cast (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 1037:
# bits1 = n + # bits0 ∧ # bits0 ≤ # bits1, # bits0 < # bits1 ⊦ bits1 = [], bits0 = [], bits2 + bits1 = [], bits1 = mklist(false, n) + mklist(false, # bits0), true ∈ bits1, bits0.first

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