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Proof step 37 from proof BFS-returns-fail-implies-not-reachable (previous step)

∀ n. ¬ reach(source, dest, n), done0 ↔ false, n0 = 0, S = ∅, S0 = {source} , S1 = {source} ⊦ [while S0 ≠ ∅ ∧ ¬ done0 do { choose v with v ∈ S0 in if v = dest then done0 := true else { S0 := S0 -- v ; ADD(succ(v); S1, S) } ; if S0 = ∅ then S0 := S, S := ∅, n0 := n0 + 1 }] [norfail0 := (done0 ⊃ some(n0); fail)] norfail0 = fail

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
S0 = ∅ ++ source, S1 = ∅ ++ source, S = ∅, n0 = 0, ¬ done0, ∀ n. ¬ reach(source, dest, n) ⊦ [while S0 ≠ ∅ ∧ ¬ done0 do { choose v with v ∈ S0 in if v = dest then done0 := true else { S0 := S0 -- v ; ADD(succ(v); S1, S) } ; if S0 = ∅ then S0 := S, S := ∅, n0 := n0 + 1 }] [norfail0 := (done0 ⊃ some(n0); fail)] norfail0 = fail

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (∅ ++ a) = 1], [CSIMPFORWARD : ⊦ s = ∅ ++ a → # s = 1], [CSIMPSEQ : ⊦ {a} = ∅ ++ a])]]