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Proof step 23 from proof ll-trav2-next (conclusion)

r2 ≠ null ⊦ (ll-trav(r0, r1, r2, x) * P)(H) ∧ H[r2] = a × r → (¬ (ll-trav(r0, r2, r, x) * P)(H) ↔ false)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : 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)))], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ a + x = a ' + x])]]