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Proof step 12 from proof linearity-path (previous step)

path(H[r].nxt ' + y1, H), r ∈ H, path(H[r].nxt ' + x0, H), ∀ r, H, y. path(r ' + x0, H) ∧ path(r ' + y, H) → x0 = y ∨ (∃ r0, y0. x0 = y + r0 ' + y0) ∨ (∃ r0, x1. y = x0 + r0 ' + x1) ⊦ x0 = y1, r = null, ∃ r0, y. x0 = y1 + r0 ' + y, ∃ r0, x. y1 = x0 + r0 ' + x

User applied rule all left

And obtained the following new goals

Proof step 13:
path(H[r].nxt ' + y1, H), r ∈ H, path(H[r].nxt ' + x0, H), path(H[r].nxt ' + x0, H) ∧ path(H[r].nxt ' + y1, H) → x0 = y1 ∨ (∃ r0, y0. x0 = y1 + r0 ' + y0) ∨ (∃ r0, x1. y1 = x0 + r0 ' + x1) ⊦ x0 = y1, r = null, ∃ r0, y. x0 = y1 + r0 ' + y, ∃ r0, x. y1 = x0 + r0 ' + x

Rule argument

pos: left 4 terms: H[r].nxt, H, y1 abort: F discard: T computed: T

Additional information

Used terms: H[r].nxt, H, y1