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Proof step 6 from proof mode-02-01 (previous step)

⊦ exactreftype(val, mkarraytype(ty), st[_mode, val0]) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st[_mode, val0] ∧ is_arrayref(val .refval, i, st[_mode, val0]) ↔ exactarray(val, ty, i, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 5:
⊦ is_referencevalue(val) ∧ val .refval ∈ st ∧ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = mkarraytype(ty) ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ st ∧ st[val .refval -- _length] = intval(i) ∧ is_arrayref(val .refval, i, st) ↔ exactarray(val, ty, i, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arrayref(r, i, st[_mode, val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ r ≠ jvmref → (st[_mode, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r ≠ jvmref → ( r -- sk ∈ st[_mode, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ (st[_mode, val][r -- _type]) = st[r -- _type]], [CSIMPSEQ : ⊦ r -- _type ∈ st[_mode, val] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ r ≠ jvmref → (r ∈ st[_mode, val] ↔ r ∈ st)])]]