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Proof step 46 from proof hasSharing-pathex (previous step)

refs1 + r0 ' = r1 ' + refs0, st[r -- i '] = refval(r1), is_array(str, r, st), hasSharing(r0, st), i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st, r, str, refs. # refs < # (r1 ' + refs0) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ refs0 = [], r = jvmref, hasSharing(r, st), r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
refs1 + r0 ' = r1 ' + refs0, st[r -- i '] = refval(r1), is_array(str, r, st), hasSharing(r0, st), i < st[r -- _length] .intval, validrefs(str, r1 ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, r0 ∈ refs0, r1 ∈ refs1, ∀ st, r, str, refs. # refs < # (r1 ' + refs0) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ refs0 = [], r = jvmref, hasSharing(r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r ' + refs = refs0 + r0 ' ∧ refs ≠ [] → r ∈ refs0 ∧ r0 ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ refs + r ' = refs0 + refs1 ∧ ¬ r ∈ refs1 → refs1 = []])]]