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Proof step 22 from proof isarray-put-array-badindex (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), r0 -- _length ∈ st[r -- i ', val], is_arrayref(r0, i0, st[r -- i ', val]), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, r0 -- _length ∈ st, r0 ∈ st[r -- i ', val], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ okreftype(refval(r0), mkarraytype(ty), st), r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: okreftype antecedent: succedent: okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ ( val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) substlist: [st, ty, val] → [st, mkarraytype(ty), refval(r0)] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-92, ⊦ is_typevalue(typeval(ty))], [CSIMPNAMEDSEQ : javavalue, , sel-11, ⊦ typeval(ty) .type = ty], [CSIMPNAMEDSEQ : typefuns, , subarray1, ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPNAMEDSEQ : typefuns, , ref, ⊦ ty ≤ ty])], [EXTRATERMS : (st, mkarraytype(ty), refval(r0))]]