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Proof step 30 from proof legal-noncylic-equiv-reaches-null (previous step)

∀ H, r. legal(H) ∧ r ∈ H → r = null ∨ (∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null) ∨ (∃ r0. reachable-n(H, n0, r, r0)), legal(H), r ∈ H ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable-n(H, n0 +1, r, r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
legal(H), r ∈ H, ∀ H, r. legal(H) ∧ r ∈ H → r = null ∨ (∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null) ∨ (∃ r0. reachable-n(H, n0, r, r0)) ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable-n(H, n0 + 1, r, r0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m +1 = m + 1])]]