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Proof step 25 from proof pathex-put-pathex-array-refval (previous step)

¬ r0 -- i0 ' ≠ r0 -- i ', st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r0 -- i0 ']) = refval(r), validrefs(str, r ' + refs, ty, st), 0 ≤ i0, 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), is_array(str, r0, st[r0 -- i ', refval(r2)]), i0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = r, r0 = (r ' + refs) .last, r0 = jvmref, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r2, (r ' + refs) .last, st), path∃(str, r0, (r ' + refs) .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
st[r0 -- _type] .type = mkarraytype(ty), validrefs(str, r ' + refs, ty, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r, ty, st), is_array(str, r0, st), is_array(str, r0, st[r0 -- i ', refval(r)]), i < st[r0 -- _length] .intval, r = jvmref → is_reftype(ty) ⊦ r0 = r, r0 = (r ' + refs) .last, r0 = jvmref, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r, (r ' + refs) .last, st), path∃(str, r0, (r ' + refs) .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , zero-gels-04, ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDFORWARD : oelem, intlista, lel, ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPNAMEDSEQ : storekey, , inj-04, ⊦ i ' = i0 ' ↔ i = i0], [CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]