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Proof step 12 from proof orderedl-at (previous step)

ordered(ixs, x), n < # ixs ⊦ ixs = [], ordered(ixs[n], x)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 11:
∀ x, n. ordered(ixs0, x) ∧ n < # ixs0 → ixs0 = [] ∨ ordered(ixs0[n], x), ordered(ix + ixs0, x), n < #(ix + ixs0) ⊦ ix + ixs0 = [], ordered((ix + ixs0)[n], x)

Rule argument

term:ixs

Additional information

[Concretesimprules((Csimpgen(illist freely generated by [], +;)))]