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Proof step 2 from proof disjoint-forward-array-01 (previous step)

disjoint(str, r ' + r1 ', st), i < st[r1 -- _length] .intval, is_arraytype(st[r1 -- _type] .type), 0 ≤ i, 0 < st[r1 -- _length] .intval ⊦ r1 = jvmref, r = r1, junkref(str, r1, st), disjoint(str, r ' + st[r1 -- i '] .refval ', st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: disjoint-forward-array-02 antecedent: succedent: r ∈ refs ∧ r1 ∈ refs ∧ r ≠ r1 ∧ ¬ junkref(str, r1, st) ∧ ¬ disjoint (str, (refs -l r1) + st[r1 -- i '] .refval, st) ∧ 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ r1 ≠ jvmref ∧ is_arraytype(st[r1 -- _type] .type) → ¬ disjoint(str, refs, st) substlist: [r, refs, r1, str, st, i] → [r, r ' + r1 ', r1, str, st, i] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, in-01, ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPNAMEDSEQ : list, references, in-17, ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPNAMEDSEQ : list-del, references, del-n, ⊦ r ≠ r0 → (r0 ' + refs) -l r = r0 ' + (refs -l r)], [CSIMPNAMEDSEQ : list-del, references, one, ⊦ r ' -l r = []], [CSIMPNAMEDSEQ : list, references, app, ⊦ refs + [] = refs], [CSIMPNAMEDSEQ : list, references, Last, ⊦ refs + r = refs + r '], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (r, r ' + r1 ', r1, str, st, i)]]