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Proof step 8 from proof refine-add (previous step)

prefixn(h, xs1 + ys) = prefixn(h, xs0), xs = xs1, xs_len = # xs1, # xs1 < h, # xs1 + # ys ≤ # xs0, ys = [] ∨ # ys = h ⊦ ⟨if xs_len + 1 = h then {ys := a + xs; xs_len := 0; xs := []} else {xs := a + xs; xs_len := 1 + xs_len}⟩ (prefixn(h, xs + ys) = prefixn(h, a ' + xs0) ∧ # xs + # ys ≤ # xs0 + 1)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 9:
xs_len + 1 = h, prefixn(h, xs1 + ys) = prefixn(h, xs0), xs = xs1, xs_len = # xs1, # xs1 < h, # xs1 + # ys ≤ # xs0, ys = [] ∨ # ys = h ⊦ ⟨ys := a + xs; xs_len := 0; xs := []⟩ (prefixn(h, xs + ys) = prefixn(h, a ' + xs0) ∧ # xs + # ys ≤ # xs0 + 1)
Proof step 21:
prefixn(h, xs1 + ys) = prefixn(h, xs0), xs = xs1, xs_len = # xs1, # xs1 < h, # xs1 + # ys ≤ # xs0, ys = [] ∨ # ys = h ⊦ ⟨xs := a + xs; xs_len := 1 + xs_len⟩ (prefixn(h, xs + ys) = prefixn(h, a ' + xs0) ∧ # xs + # ys ≤ # xs0 + 1), xs_len + 1 = h

Rule argument

pos: right 1

Proof step 8 from proof refine-add (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

Additional information