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Proof step 24 from proof okarray-primput (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ okarray(refval(r), ty, i, st) → is_typevalue(st[r -- _type])
Proof step 5:
⊦ 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 6:
⊦ oktype(val0, ty, st[r1 -- sk, val]) ↔ oktype(val0, ty, st)
Proof step 23:
0 < st[r -- _length] .intval, okprimtype(val, ty), j < st[r -- _length] .intval, okarray(refval(r), ty, st[r -- _length] .intval, st), 0 ≤ j ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st[r -- j ', val]) ∧ r -- _length ∈ st ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r -- _length] .intval → oktype((j0 = j ⊃ val; st[r -- j0 ']), ty, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : is_integervalue(val) ⊦ intval(val .intval) = val], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ okprimtype(val, ty) → (ty0 ≤ ty ↔ ty0 = ty)], [CSIMPSEQ : ⊦ i ≤ j → ( is_arrayref (r, i, st[r0 -- j ', val]) ↔ is_arrayref(r, i, st))], [CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]