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Proof step 11 from proof modnotreachable-reachable-rev (previous step)

path(H[r].nxt ' + x0, H[r0, ce]), (H[r].nxt ' + x0).last ∈ H[r0, ce], r0 ∈ H, r ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0[r3, ce0]) ∧ r3 ∈ H0 → reachable(r2, r3, H0) ∨ reachable(r2, (r2 ' + x0).last, H0) ⊦ r = r0, r = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, r0, H)

User applied rule all left

And obtained the following new goals

Proof step 12:
path(H[r].nxt ' + x0, H[r0, ce]), r ∈ H, r0 ∈ H, (H[r].nxt ' + x0).last ∈ H[r0, ce], path(H[r].nxt ' + x0, H[r0, ce]) ∧ r0 ∈ H → reachable(H[r].nxt, r0, H) ∨ reachable(H[r].nxt, (H[r].nxt ' + x0).last, H) ⊦ r = null, r = r0, reachable(r, r0, H), reachable(r, (H[r].nxt ' + x0).last, H)

Rule argument

pos: left 5 terms: H[r].nxt, H, r0, ce abort: F discard: T computed: T

Additional information

Used terms: H[r].nxt, H, r0, ce