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Proof step 14 from proof modnotreachable-reachable (previous step)

(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) → reachable(r2, r3, H0) ∨ path(r2 ' + x0, H0[r3, ce0]) ⊦ r = null, r = r1, reachable(r, r1, H), path(H[r].nxt ' + x0, H[r1, ce])

User applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: H[r].nxt, H, r1, ce abort: F discard: T computed: T

Additional information

Used simplifier rules: fromnext-reachable-rev: ⊦ reachable(H[r].nxt, r0, H) ∧ r ≠ r0 ∧ r ≠ null ∧ r ∈ H → (¬ reachable(r, r0, H) ↔ false); Used terms: H[r].nxt, H, r1, ce