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Proof step 29 from proof okarray-put-okval-01 (previous step)

okval(val0, ty), okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(j) ∈ st ∧ 0 ≤ j ∧ is_arrayref(val .refval, j, st) ∧ (∀ j0. 0 ≤ j0 ∧ j0 < j → oktype(st[val .refval -- j0 '], ty, st)) ⊦ okarray(val, ty, j, st[r -- i ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ 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 3:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 28:
st[val .refval -- _length] = intval(j), is_arrayref(val .refval, j, st), okval(val0, ty), is_referencevalue(val), val .refval -- _type ∈ st, is_typevalue(st[val .refval -- _type]), is_arraytype(st[val .refval -- _type] .type), st[val .refval -- _type] .type .type ≤ ty, val .refval -- _length ∈ st, 0 ≤ j, val .refval ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[val .refval -- j0 '], ty) ⊦ val .refval = jvmref, okarray(val, ty, j, st[r -- i ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty])]]