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Proof step 34 from proof okarray-put-07 (previous step)

okreftype(refval(r0), mkarraytype(ty), st) ∧ refval(r0) .refval ≠ jvmref ∧ (refval(r0) .refval -- _length) × intval(st[r0 -- _length] .intval) ∈ st ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(refval(r0) .refval, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[refval(r0) .refval -- j '], ty, st)) ⊦ r0 = jvmref, r = r0, (0 ≤ j ∧ j < st[r0 -- _length] .intval → okval(st[r0 -- j '], ty)) ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ ¬ st[r0 -- _length] .intval < 0 ∧ st[r0 -- _length] = intval(st[r0 -- _length] .intval) ∧ r0 -- _length ∈ st ∧ is_arraytype(st[r0 -- _type] .type) ∧ r0 -- _type ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
⊦ 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 28:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 33:
r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), st[r0 -- _type] .type .type ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, st[r0 -- _length] .intval, st), j < st[r0 -- _length] .intval, r0 ∈ st, 0 ≤ st[r0 -- _length] .intval, 0 ≤ j, 0 < st[r0 -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r = r0, r0 = jvmref, okval(st[r0 -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : is_integervalue(val) ⊦ intval(val .intval) = val], [CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [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], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]