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Proof step 28 from proof okarray-putba (previous step)

⊦ r = r0, okreftype(refval(r0), mkarraytype(ty), putByteArray(bytes, r, i1, st)) ∧ refval(r0) .refval ≠ jvmref ∧ (refval(r0) .refval -- _length) × intval(i) ∈ putByteArray(bytes, r, i1, st) ∧ 0 ≤ i ∧ is_arrayref(refval(r0) .refval, i, putByteArray(bytes, r, i1, st)) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(putByteArray(bytes, r, i1, st)[refval(r0) .refval -- j '], ty, putByteArray(bytes, r, i1, st))) ↔ okarray(refval(r0), ty, i, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ 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)
Proof step 4:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 27:
⊦ r = r0, r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_arraytype(st[r0 -- _type] .type) ∧ st[r0 -- _type] .type .type ≤ ty ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ st[r0 -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(r0, i, putByteArray(bytes, r, i1, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty)) ↔ okarray(refval(r0), ty, i, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (putByteArray(bytes, r, j, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (putByteArray(bytes, r, i, st) [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ (putByteArray(bytes, r, i, st) [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPSEQ : ⊦ r ≠ r0 → ( r0 -- sk ∈ putByteArray (bytes, r, j, st) ↔ r0 -- sk ∈ st)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]