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Proof step 103 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)]), ∃ refs2, refs1. refs0 = refs2 + (r0 + refs1), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 102:
st[r0 -- _type] .type = mkarraytype(ty), list2set(refs1) ∩ list2set(refs) = ∅, validrefs(str, r ' + refs1 + r0 ' + refs, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, r2 = jvmref → is_reftype(ty) ⊦ r = (r0 ' + refs) .last, r0 = jvmref, r = r0, r0 ∈ refs, r0 ∈ refs1, dups(refs), dups(refs1), path∃(str, r, (r0 ' + refs) .last, st), path∃(str, r2, (r0 ' + refs) .last, st), r ∈ refs1, r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : setlist, references, dups-03, ⊦ ¬ dups(refs) ∧ ¬ dups(refs0) → ( dups(refs + refs0) ↔ list2set(refs) ∩ list2set(refs0) ≠ ∅)], [CSIMPNAMEDFORWARD : list-dup, references, a, ⊦ ¬ dups(refs + refs0) → ¬ dups(refs) ∧ ¬ dups(refs0)], [CSIMPNAMEDSEQ : list, references, in-01, ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPNAMEDSEQ : list, references, in-append, ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPNAMEDSEQ : list-dup, references, f-01, ⊦ dups(refs + r ' + refs0) ↔ r ∈ refs ∨ r ∈ refs0 ∨ dups(refs + refs0)], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list-last, references, lapp-01, ⊦ (refs + r ' + refs0) .last = (r ' + refs0) .last], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]