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Proof step 43 from proof validrefs-put-badarrayfield-01 (previous step)

0 ≤ i, 0 < st[r -- _length] .intval, junkref(str, st[r -- i '] .refval, st), is_arraytype(st[r0 -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st) ⊦ fs ' = _type, fs ' = _length, r = jvmref, junkref(str, r, st[r0 -- fs ', val]), junkref(str, r, st), dups((st[r -- i '] .refval ' + refs) .butlast), r ∈ (st[r -- i '] .refval ' + refs) .butlast, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty0] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty0)]]