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Proof step 17 from proof linearity-path (previous step)

y1 = x0 + r1 ' + x, path(H[r].nxt ' + y1, H), r ∈ H, path(H[r].nxt ' + x0, H) ⊦ x0 = y1, r = null, ∃ r0, y. x0 = y1 + r0 ' + y, ∃ r0, x. y1 = x0 + r0 ' + x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
path(H[r].nxt ' + x0 + r1 ' + x, H), r ∈ H, path(H[r].nxt ' + x0, H) ⊦ r = null, ∃ r0, x1. r1 ' + x = r0 ' + x1

Rule argument

Additional information

Used simplifier rules: app-01: ⊦ x0 + x1 = x0 + x2 ↔ x1 = x2; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%app-04: ⊦ x0 = x0 + x1 ↔ x1 = []; from specification list[reflist]