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Proof step 299 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), # bits = n0 + # bits0, # bits0 < n, # bits < n, true ∈ bits, bits0.first, # bits0 ≤ # bits ⊦ bits = [], bits0 = [], mklist(true, n - # bits0) + bits0 = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), false ∈ bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 300:
n = n1 + # bits0 ∧ # bits0 ≤ n, n = # fillsgn(n, bits), # bits = n0 + # bits0, # bits0 < n, # bits < n, true ∈ bits, bits0.first, # bits0 ≤ # bits ⊦ bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), false ∈ bits

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bits0, n1] 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, # bits0, n1