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Proof step 15 from proof refine-add (previous step)

xs1 + prefixn(# xs1 + 1 - # xs1, ys) = prefixn(# xs1 + 1, xs0), # xs1 ≤ # xs0, # xs1 + # ys ≤ # xs0, # xs1 ≤ # xs1 + 1, ys = [] ∨ # ys = # xs1 + 1 ⊦ xs1 = prefixn(# xs1, xs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
xs1 + prefixn(1, ys) = prefixn(# xs1 + 1, xs0), # xs1 + # ys ≤ # xs0, # xs1 ≤ # xs0, ys = [] ∨ # ys = # xs1 + 1 ⊦ xs1 = prefixn(# xs1, xs0)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - m = n; (s)