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Proof step 19 from proof BFS-returns-fail-implies-not-reachable (previous step)

⟪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) ⊦ [ADD(succ(v); S1, S)] [S0 := S0 -- v ; if S0 = ∅ then S0 := S, S := ∅, n0 := n0 + 1] ((∀ n. ¬ reach(source, dest, n)) ∧ INV(S0, S, S1, n0, source))

Heuristic contract and execute applied rule execute call

And obtained the following new goals

Proof step 18:
〈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) ⊦ [S0 := S0 -- v] [if S0 = ∅ then S0 := s0, s0 := ∅, n0 := n0 + 1] ((∀ n. ¬ reach(source, dest, n)) ∧ INV(S0, s0, s, n0, source))

Rule argument

[fmaposlist-arg: (pos: left 1, pos: right 1)]

Additional information

[[CONCRETESIMPRULES : ()]]