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Proof step 342 from proof bitsand-cast (previous step)

mklist(false, # bits) = bits, # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], mklist(false, n) = mklist(bits.first, n - # bits) + bits, bits = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 343:
n = n0 + # bits ∧ # bits ≤ n, mklist(false, # bits) = bits, # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], mklist(false, n) = mklist(bits.first, n0) + bits, bits = []

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bits, n0] 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: n, # bits, n0