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Proof step 20 from proof legal-noncylic-equiv-reaches-null (previous step)

legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H

User applied rule cut formula

And obtained the following new goals

Proof step 12:
H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H
Proof step 19:
legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ H[r0] .nxt = null, r = null, reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H

Rule argument

[fma-arg: H[r0] .nxt = null]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (H[r0] .nxt = null)]]