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Proof step 359 from proof bitsand-cast (previous step)

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

User applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits0, n0