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Proof step 6 from proof path-modify-strong (previous step)

r ∈ H, r0 ∈ H, ∀ r3, H0, r4, ce0. r3 ∈ H0 → (path((H[r].nxt ' + x) + r4 ', H0[r3, ce0]) ↔ path((H[r].nxt ' + x) + r4 ', H0)) ∨ r3 = H[r].nxt ∨ r3 ∈ x ⊦ r0 = H[r].nxt, r = null, path(H[r].nxt ' + x + r1 ', H[r0, ce]) ↔ path(H[r].nxt ' + x + r1 ', H), r0 = r, r0 ∈ x

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: r0, H, r1, ce abort: F discard: T computed: T

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: r0, H, r1, ce