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Proof step 17 from proof BFS-returns-fail-implies-not-reachable (previous step)

〈ADD(succ(v); S1, S)〉 (S1 = s ∧ S = s0), ⟪ADD(succ(v); S1, S)⟫ INV(S0 -- v, S, S1, n0, source), S0 ≠ ∅, # S0 ≠ 0, v ≠ dest, INV(S0, S, S1, n0, source), v ∈ S0, ∀ n. ¬ reach(source, dest, n), INV(S0 -- v, s0, s, n0, source), S2 = S0 -- v ⊦ [if S2 = ∅ then S2 := s0, s0 := ∅, n0 := n0 + 1] ((∀ n. ¬ reach(source, dest, n)) ∧ INV(S2, s0, s, n0, source))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
〈ADD(succ(v); S1, S)〉 (S1 = s ∧ S = s0), ⟪ADD(succ(v); S1, S)⟫ INV(S0 -- v, S, S1, n0, source), S2 = S0 -- v, S0 ≠ ∅, # S0 ≠ 0, v ≠ dest, INV(S0, S, S1, n0, source), v ∈ S0, INV(S0 -- v, s0, s, n0, source), ∀ n. ¬ reach(source, dest, n) ⊦ [if S0 = ∅ ++ v then S2 := s0, s0 := ∅, n0 := n0 + 1] ((∀ n. ¬ reach(source, dest, n)) ∧ INV(S2, s0, s, n0, source))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a])]]