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Proof step 3 from proof ADD-preserves-INV-INVR (previous step)

⟪ADD(succ(v); V, N)⟫ (N = N0 ∪ (succ(v) \ V0) ∧ V = V0 ∪ succ(v)), ⟪ADD(succ(v); V, N)⟫ INV(C -- v, N, V, n, source), 〈ADD(succ(v); V, N)〉 (V = S ∧ N = S0), C ≠ ∅, v ≠ dest, # C ≠ 0, INV(C -- v, S0, S, n, source), INVR(C, N, V, n, n0, source, dest), v ∈ C, INV(C, N, V, n, source), ¬ INVR(C -- v, S0, S, n, n0, source, dest), V0 = V, N0 = N ⊦

User applied rule contract call left

And closed the goal!

Rule argument

[fmaposlist-arg: (pos: left 1, pos: left 3)]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ INVR (C, N, V, n, n0, source, dest) ∧ INV(C, N, V, n, source) ∧ v ∈ C ∧ v ≠ dest → ( ¬ INVR (C -- v, N ∪ (succ(v) \ V), V ∪ succ(v), n, n0, source, dest) ↔ false)], [CSIMPSEQ : ⊦ (s ∪ s0) ∪ s1 = s ∪ s0 ∪ s1], [CSIMPSEQ : ⊦ s ∪ s0 = s0 ∪ s])]]