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Proof step 21 from proof okarray-primput (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ 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 20:
0 ≤ j0, 0 ≤ st[r -- _length] .intval, r ∈ st, j0 < st[r -- _length] .intval, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, j < st[r -- _length] .intval, okprimtype(val, st[r -- _type] .type .type), 0 < st[r -- _length] .intval, 0 ≤ j, ∀ j1. ¬ j1 < 0 ∧ ¬ st[r -- _length] .intval ≤ j1 → oktype(st[r -- j1 '], st[r -- _type] .type .type, st) ⊦ r = jvmref, oktype((j0 = j ⊃ val; st[r -- j0 ']), st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

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