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Proof step 37 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), ∀ 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)) ⊦ validrefs(str, r1 ' + refs0 + r0 ', st[r1 -- _type] .type, st) ∧ hasSharing((refs0 + r0 ') .last, st), r = jvmref, hasSharing(r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
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), ∀ 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), validrefs(str, r1 ' + refs0 + r0 ', st[r1 -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (refs + r ') .last = r])]]