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Proof step 31 from proof k-reachable-def (previous step)

reachable-n(H, n, r, r0), r ∈ H ⊦ n = 0, r = null, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0

User applied rule structural induction

And obtained the following new goals

Proof step 32:
reachable-n(H, n0 +1, r, r0), r ∈ H, ∀ H, r, r0. reachable-n(H, n0, r, r0) ∧ r ∈ H → n0 = 0 ∨ r = null ∨ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) ⊦ n0 +1 = 0, r = null, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;