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

closed(H), path(x, r0, r1, H), r0 ∈ H, r1 ∈ H, H[r1] = Node(a, succ) ⊦ ⟪eval#(r0, x, H; a?)⟫ (a? = some(a))

Heuristic induction applied rule induction

And obtained the following new goals

Proof step 19:
∀ x0, H, r0, r1, a, succ. # x0 < # x → closed(H) ∧ path(x0, r0, r1, H) ∧ r0 ∈ H ∧ r1 ∈ H ∧ H[r1] = Node(a, succ) → ⟪eval#(r0, x0, H; a?)⟫ (a? = some(a)), closed(H), path(x, r0, r1, H), r0 ∈ H, r1 ∈ H, H[r1] = Node(a, succ) ⊦ ⟪eval#(r0, x, H; a?)⟫ (a? = some(a))

Rule argument

indvar:# x wfpred:<

Additional information

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