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Proof step 7 from proof lls-consecutive (previous step)

(lls(r0, r1, x) * lls(r1, r2, y) * P)(H) ⊦ (lls(r0, r2, x + y) * P)(H)

User applied rule structural induction

And closed the goal!

Rule argument

[VARWITHVARSEQSARG : x, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : lls-base, , , ⊦ lls(r0, r1, []) = (emp ∧ ⌜r0 = r1⌝ )], [CSIMPGEN : list generated by [], +;], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPSEQ : ⊦ (⌜bv⌝ ∧ P0) * P1 = (⌜bv⌝ ∧ P0 * P1)], [CSIMPSEQ : ⊦ emp * P = P], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2)], [CSIMPSEQ : ⊦ (P0 ∧ P1) = (P1 ∧ P0)], [CSIMPSEQ : ⊦ (P0 ∧ P1)(H) ↔ ¬ ¬ (P0(H) ∧ P1(H))], [CSIMPSEQ : ⊦ ⌜bv⌝ (H) ↔ bv], [CSIMPSEQ : ⊦ [] + x = x], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z])]]