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Proof step 8 from proof linearity-path (previous step)

path(H[r].nxt ' + x0, H), r ∈ H, path(r ' + y, 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) ⊦ r = null, H[r].nxt ' + x0 = y, ∃ r1, x. y = (H[r].nxt ' + x0) + r1 ' + x, ∃ r1, y0. H[r].nxt ' + x0 = y + r1 ' + y0

User applied rule constructor cut

And obtained the following new goals

Proof step 9:
y = [], path(H[r].nxt ' + x0, H), r ∈ H, path(r ' + y, 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) ⊦ r = null, H[r].nxt ' + x0 = y, ∃ r1, x. y = (H[r].nxt ' + x0) + r1 ' + x, ∃ r1, y0. H[r].nxt ' + x0 = y + r1 ' + y0
Proof step 11:
y = r2 + y1, path(H[r].nxt ' + x0, H), r ∈ H, path(r ' + y, 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) ⊦ r = null, H[r].nxt ' + x0 = y, ∃ r1, x. y = (H[r].nxt ' + x0) + r1 ' + x, ∃ r1, y0. H[r].nxt ' + x0 = y + r1 ' + y0

Rule argument

var: y

Additional information

Used simplifier rules: reflist freely generated by [], +;;