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Proof step 9 from proof pathex-put-pathex-array-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-is-junk antecedent: succedent: r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st) substlist: [st, ty, refs, r, str] → [st[r0 -- i ', refval(r2)], mkarraytype(ty), refs0, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_valid_ref-01, ⊦ ¬ is_array(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_obj(str, r, st))], [CSIMPNAMEDSEQ : addfuns, , is_obj-put-index, ⊦ is_obj (str, r, st[r0 -- i ', val]) ↔ is_obj(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , is_obj-type-02, ⊦ st[r -- _type] .type = mkarraytype(ty) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st[r0 -- i ', refval(r2)], mkarraytype(ty), refs0, r0, str)]]