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Proof step 15 from proof junkref-primarray-level-01 (previous step)

st[r -- i '] = refval(r0), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_valid_ref(str1, r0, st), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str1, r, st), has_classtype(st[r -- _type] .type .type), ∀ str1, st0, r1, str, refs. # refs < # (r0 + refs1) → ( junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → has_classtype(st0[r1 -- _type] .type) ∨ junkrefs(str1, r1 ' + refs, st0[r1 -- _type] .type, st0)) ⊦ r0 = jvmref, r = jvmref, st[r -- _type] .type .type = st[r0 -- _type] .type, junkrefs(str1, r0 ' + refs1, st[r -- _type] .type .type, st), has_classtype(st[r -- _type] .type)

User applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

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