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Proof step 18 from proof okarray-put-08 (previous step)

⊦ fs ' = _length, fs ' = _type, okreftype(val, mkarraytype(ty), st[r -- fs ', val0]) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st[r -- fs ', val0] ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st[r -- fs ', val0]) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- fs ', val0][val .refval -- j '], ty, st[r -- fs ', val0])) ↔ okarray(val, 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:
⊦ sk0 ≠ _type → (oktype(val, ty, st[r -- sk0, val0]) ↔ oktype(val, ty, st))
Proof step 5:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 17:
⊦ fs ' = _length, fs ' = _type, is_referencevalue(val) ∧ val .refval -- _type ∈ st[r -- fs ', val0] ∧ is_typevalue(st[val .refval -- _type]) ∧ is_arraytype(st[val .refval -- _type] .type) ∧ st[val .refval -- _type] .type .type ≤ ty ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ st[r -- fs ', val0] ∧ st[val .refval -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[val .refval -- j '], ty)) ↔ okarray(val, ty, i, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_arrayref (r, i, st[r0 -- fs ', val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])]]