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Proof step 9 from proof ll-trav2-end (previous step)

H[r2] = a × null, ((ll-trav(r0, r1, r2, x) * P))(H) ⊦ r1 = null, r2 = null, ∃ y, b. x = y + b ' + a ' ∧ ((lls(r0, r1, y) * r1 => b × r2 * r2 => a × null * P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
H[r2] = a × null, ((lls(r0, r1, x0) * r1 => a0 × r2 * lls(r2, null, x1) * P))(H) ⊦ r1 = null, r2 = null, ∃ y, b. x0 + a0 ' + x1 = y + b ' + a ' ∧ ((lls(r0, r1, y) * r1 => b × r2 * r2 => a × null * P))(H)

Rule argument

Additional information

Used simplifier rules: ll-trav2-nonnull-def: ⊦ r1 ≠ null → ( ((ll-trav(r0, r1, r2, x) * P))(H) ↔ (∃ x0, x1, a. x = x0 + (a + x1) ∧ ((lls(r0, r1, x0) * r1 => a × r2 * lls(r2, null, x1) * P) )(H)));%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)