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Proof step 31 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), st[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, i0 = i, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r2, (r ' + refs) .last, st), r0 ' + r ' + refs ≠ [] ∧ (r0 ' + r ' + refs) .first = r0 ∧ (r0 ' + r ' + refs) .last = (r ' + refs) .last ∧ validrefs(str, r0 ' + r ' + refs, st[(r0 ' + r ' + refs) .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
st[r0 -- _type] .type = mkarraytype(ty), st[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, i0 = i, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r2, (r ' + refs) .last, st), validrefs(str, r0 ' + r ' + refs, mkarraytype(ty), st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list-last, references, l-05, ⊦ (r ' + r0 ' + refs) .last = (r0 ' + refs) .last], [CSIMPNAMEDSEQ : list, references, c-08, ⊦ (r ' + refs) .first = r], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e, ⊦ r ' ≠ []], [CSIMPNAMEDSEQ : list, references, app-02-ant, ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]