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Proof step 10 from proof ll-trav2-end (previous step)

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)

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
H[r2] = a × null, x1 = a1 + x, ((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

var: x1

Additional information

Used simplifier rules: lls-base: ⊦ lls(r0, r1, []) = (emp ∧ ⌜r0 = r1⌝ );%list freely generated by [], +;;% ⊦ ⌜false⌝ = false; (s)% ⊦ (false ∧ P) = false; (s)%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2); from specification heap-sep%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); from specification heap-sep% ⊦ false * P = false; (s)%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep% ⊦ ¬ false(H); (s)