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Proof step 140 from proof BFS-correct-if-reachable (previous step)

S0 = ∅ ++ source, S1 = ∅ ++ source, S = ∅, n0 = 0, ¬ done0, reach(source, dest, n), ¬ reach<(source, dest, n), INVR(S0, S, S1, n0, n, source, dest), INV(S0, S, S1, n0, source), done0 → dest ∈ S0, S0 = ∅ → S = ∅ ⊦ ⟪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 = some(n)

User applied rule weakening

And obtained the following new goals

Proof step 139:
INVR(S0, S, S1, n0, n, source, dest), INV(S0, S, S1, n0, source), done0 → dest ∈ S0, S0 = ∅ → S = ∅ ⊦ ⟪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 = some(n)

Rule argument

[fmaposlist-arg: (pos: left 1, pos: left 2, pos: left 3, pos: left 4, pos: left 5, pos: left 6, pos: left 7) ]

Additional information

[[CONCRETESIMPRULES : ()]]