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Proof step 6 from proof ll-trav2-next (previous step)

H[r0] = a × r, ((lls(r0, null, x) * P))(H) ⊦ r0 = null, x = [] + x.head ' + x.tail ∧ ((lls(r0, r0, []) * r0 => x.head × r * lls(r, null, x.tail) * P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
H[r0] = a × r, ((lls(r0, null, x) * P))(H) ⊦ r0 = null, x = x.head ' + x.tail ∧ ((r0 => x.head × r * lls(r, null, x.tail) * P))(H)

Rule argument

Additional information

Used simplifier rules: lls-base: ⊦ lls(r0, r1, []) = (emp ∧ ⌜r0 = r1⌝ );%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep% ⊦ emp * P = P; (s)%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); from specification heap-sep%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2); from specification heap-sep% ⊦ (true ∧ P) = P; (s)% ⊦ ⌜true⌝ = true; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ [] + x = x; (s)