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Proof step 15 from proof legal-noncylic-equiv-reaches-null (previous step)

x = r + x1 ∧ x ≠ [], # x = n0 + 1, legal(H), r ∈ H, path(x, H) ⊦ H[x .last] .nxt = null, r = null, n0 = 0, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, x .last ≠ null ∧ x .last ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
x1 .last = null, path(r ' + x1, H), r ∈ H, legal(H) ⊦ r = null, H[null] .nxt = null, x1 = [], ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ x0 ≠ [] → (r ' + x0) .last = x0 .last], [CSIMPSEQ : ⊦ # x0 = 0 ↔ x0 = []], [CSIMPSEQ : ⊦ path(r ' + x, H) → (¬ (r ' + x) .last ∈ H ↔ false)], [CSIMPSEQ : ⊦ r ' + x0 ≠ []], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (x0 + x1) = # x0 + # x1], [CSIMPSEQ : ⊦ r + x0 = r ' + x0])]]