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Proof step 15 from proof validrefs-applast-array-null (previous step)

0 < st[r -- _length] .intval, 0 ≤ i, is_reftype(st[r -- _type] .type .type), i < st[r -- _length] .intval, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), okarray(r, st[r -- _type] .type .type, st), type∃(str, st[r -- _type] .type), validrefs(str, refs + r ', ty, st), r ∈ st ⊦ r = jvmref, st[r -- _type] .type .type .jtelemtype = void_type, st[r -- _type] .type .type .jtelemtype = abstract_type, is_referencevalue(st[r -- i ']), validrefs(str, refs + r ' + jvmref ', ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
st[r -- _type] .type = mkarraytype(ty0), 0 < st[r -- _length] .intval, 0 ≤ i, is_reftype(ty0), i < st[r -- _length] .intval, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), okarray(r, ty0, st), type∃(str, st[r -- _type] .type), validrefs(str, refs + r ', ty, st), r ∈ st ⊦ r = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, is_referencevalue(st[r -- i ']), validrefs(str, refs + r ' + jvmref ', ty, st)

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