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Proof step 14 from proof lls-unfold-tail (previous step)

((lls(r0, r, x) * r => a × r2 * P))(H) ⊦ ((lls(r0, r2, x + a ') * P))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: lls-fold-tail seq: x ≠ [] ⊦ ((r1 => x.last × r2 * lls(r0, r1, x.butlast) * P))(H) → ((lls(r0, r2, x) * P))(H) subst: [r1, H, P, x, r2, r0] → [r, H, P, x + a ', r2, r0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ x + a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (x + a ').last = a; (s)% ⊦ (x + a ').butlast = x; (s)%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep Used terms: r, H, P, x + a ', r2, r0