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Proof step 15 from proof modnotreachable-reachable (previous step)

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

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) ↔ true); Used terms: H[r].nxt, H, r1, ce