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Proof step 6 from proof ADD-preserves-INV-INVR (previous step)

⟪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) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
N = N0, V = V0 ⊦ ⟪ADD(S; V, N)⟫ (N = N0 ∪ (S \ V0) ∧ V = V0 ∪ S)
Proof step 5:
⟪V1 := V⟫ ⟪N1 := N⟫ ⟪ADD(succ(v); V, N)⟫ (N = N1 ∪ (succ(v) \ V1) ∧ V = V1 ∪ 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) ⊦

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: ADD-lemma antecedent: N = N0, V = V0 succedent: ⟪ADD(S; V, N)⟫ (N = N0 ∪ (S \ V0) ∧ V = V0 ∪ S) substlist: [N, N0, V, V0, S] → [N, N, V, V, succ(v)] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (N, N, V, V, succ(v))]]