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Proof step 20 from proof eval-nonexisting-path (previous step)

r0 ∈ H, closed(H), ∀ r1. ¬ path(x, r0, r1, H) ⊦ ⟪eval#(r0, x, H; a?)⟫ (a? = none)

Heuristic induction applied rule induction

And obtained the following new goals

Proof step 19:
∀ x0, r0, H. # x0 < # x → r0 ∈ H ∧ closed(H) ∧ (∀ r1. ¬ path(x0, r0, r1, H)) → ⟪eval#(r0, x0, H; a?)⟫ (a? = none), r0 ∈ H, closed(H), ∀ r1. ¬ path(x, r0, r1, H) ⊦ ⟪eval#(r0, x, H; a?)⟫ (a? = none)

Rule argument

indvar:# x wfpred:<

Additional information

[Concretesimprules((Csimplesspred(<))), Extraterms((# x))]