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Proof step 105 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ r = r0, r0 = jvmref, r = (r ' + refs0) .last, path∃(str, r2, (r ' + refs0) .last, st), path∃(str, r, (r ' + refs0) .last, st), dups(refs0), r ∈ refs0, r0 ≠ r ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 104:
st[r0 -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), r0 ∈ refs0, r2 = jvmref → is_reftype(ty) ⊦ r = r0, r0 = jvmref, r = refs0 .last, dups(refs0), r ∈ refs0, path∃(str, r2, refs0 .last, st), path∃(str, r, refs0 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list-last, references, in, ⊦ r ∈ refs → (r0 ' + refs) .last = refs .last])]]