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Proof step 5 from proof linearity (previous step)

path(r ' + x, H), reachable(r, r1, H), (r ' + x).last ∈ H, r1 ∈ H ⊦ reachable((r ' + x).last, r1, H), reachable(r1, (r ' + x).last, H)

User applied rule induction

And obtained the following new goals

Proof step 6:
path(r ' + x, H) ∧ reachable(r, r1, H) ∧ (r ' + x).last ∈ H ∧ r1 ∈ H, ∀ x0, r, H, r1. # x0 < # x → path(r ' + x0, H) ∧ reachable(r, r1, H) ∧ (r ' + x0).last ∈ H ∧ r1 ∈ H → reachable((r ' + x0).last, r1, H) ∨ reachable(r1, (r ' + x0).last, H) ⊦ reachable((r ' + x).last, r1, H) ∨ reachable(r1, (r ' + x).last, H)

Rule argument

indvar: # x wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # x