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Proof step 47 from proof disjoint-forward-array (previous step)

disjoint(str, refs, st), r ∈ refs, r1 ∈ refs, 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, (refs -l r1) + st[r1 -- i '] .refval ', st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ disjoint(str, refs, st) ↔ ¬ (∃ r, r0, r1. r ∈ refs ∧ r0 ∈ refs ∧ r ≠ r0 ∧ r1 ≠ jvmref ∧ path∃(str, r, r1, st) ∧ path∃(str, r0, r1, st))
Proof step 46:
disjoint(str, refs, st), r ∈ refs, r1 ∈ refs, 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), ∀ r, r0, r2. ¬ ( r ∈ (refs -l r1) + st[r1 -- i '] .refval ' ∧ r0 ∈ (refs -l r1) + st[r1 -- i '] .refval ' ∧ r ≠ r0 ∧ r2 ≠ jvmref ∧ path∃(str, r, r2, st) ∧ path∃(str, r0, r2, st))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: disjoint-def-pathex antecedent: succedent: disjoint(str, refs, st) ↔ ¬ (∃ r, r0, r1. r ∈ refs ∧ r0 ∈ refs ∧ r ≠ r0 ∧ r1 ≠ jvmref ∧ path∃(str, r, r1, st) ∧ path∃(str, r0, r1, st)) substlist: [st, refs, str] → [st, (refs -l r1) + st[r1 -- i '] .refval ', str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, (refs -l r1) + st[r1 -- i '] .refval ', str)]]