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Proof step 12 from proof isarray-put-samefield-01 (previous step)

okarray(r, st[r -- _type] .type .type, st[r -- mkfs(class, ty, fieldvar) ', val]), is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, oktype(val, ty, st), oktype(st[r -- mkfs(class, ty, fieldvar) '], ty, st), r -- mkfs(class, ty, fieldvar) ' ∈ st, r ∈ st ⊦ r = jvmref, mkfs(class, ty, fieldvar) ' = _type, mkfs(class, ty, fieldvar) ' = _length, is_array(r, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
st[r -- _type] .type = mkarraytype(ty0), okarray(r, ty0, st[r -- mkfs(class, ty, fieldvar) ', val]), is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, oktype(val, ty, st), oktype(st[r -- mkfs(class, ty, fieldvar) '], ty, st), r -- mkfs(class, ty, fieldvar) ' ∈ st, r ∈ st ⊦ r = jvmref, mkfs(class, ty, fieldvar) ' = _type, mkfs(class, ty, fieldvar) ' = _length, is_array(r, 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)]]