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Proof step 39 from proof hasSharing-pathex (previous step)

st[r -- i '] = refval(r1), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), hasSharing(r0, st), i < st[r -- _length] .intval, validrefs(str, (r1 ' + refs0) + r0 ', st[r -- _type] .type .type, st), hasSharing(r1, st), ∀ st, r, str, refs. # refs < # (r1 ' + refs0 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ ¬ hasSharing(r, st) ∧ st[r -- i '] = refval(r0) ∧ r ≠ jvmref ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_arraytype(st[r -- _type] .type) → ¬ hasSharing(r0, st)

Rule argument

[crewrite-arg: hasSharing-array-forward , F , [r, st, i, r0] → [r, st, i, r1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)])], [EXTRATERMS : (r, st, i, r1)]]