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Proof step 310 from proof bitsand-cast (previous step)

n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ n0 = 0, mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist(true, n1 - n0) + mklist(true, n0) + bits0), false ∈ bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 311:
n1 = n + n0 ∧ n0 ≤ n1, n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ n0 = 0, mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist(true, n) + mklist(true, n0) + bits0), false ∈ bits

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1, n0, n] rotate: T spec: nat inst: name: elim-sub

Additional information

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