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Proof step 12 from proof validref-forward-array (previous step)

st0[r -- i '] = refval(r0), 0 < st0[r -- _length] .intval, 0 ≤ i, i < st0[r -- _length] .intval, validref(str, r, mkarraytype(ty), st0), is_valid_ref(str, r, st0), is_arraytype(st0[r -- _type] .type), st0[r -- _type] .type .type ≤ ty ⊦ r = jvmref, validref(str, r0, ty, st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
st0[r -- _type] .type = mkarraytype(ty0), st0[r -- i '] = refval(r0), 0 < st0[r -- _length] .intval, 0 ≤ i, i < st0[r -- _length] .intval, validref(str, r, mkarraytype(ty), st0), is_valid_ref(str, r, st0), is_arraytype(st0[r -- _type] .type), ty0 ≤ ty ⊦ r = jvmref, validref(str, r0, ty, st0)

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st0[r -- _type] .type, ty0] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st0[r -- _type] .type, ty0)]]