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Proof step 23 from proof isarray-put-field (previous step)

is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type) ⊦ fs ' = _length, fs ' = _type, r -- _type ∈ st[r0 -- fs ', val] ∧ okarray(r, st[r -- _type] .type .type, st[r0 -- fs ', val]) ↔ r -- _type ∈ st ∧ okarray(r, st[r -- _type] .type .type, st), r = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
st[r -- _type] .type = mkarraytype(ty), is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type) ⊦ fs ' = _length, fs ' = _type, r -- _type ∈ st[r0 -- fs ', val] ∧ okarray(r, ty, st[r0 -- fs ', val]) ↔ r -- _type ∈ st ∧ okarray(r, ty, st), r = jvmref

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