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Proof step 39 from proof isarray-put-array-badindex (previous step)

okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 -- _length ∈ st ∧ is_arrayref(r0, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty)), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ r0 -- _length ∈ st[r -- i ', val] ∧ is_arrayref(r0, i0, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)), r0 = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
⊦ 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 38:
st[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), r0 ∈ st, r0 -- _type ∈ st, i < 0, 0 ≤ i0, is_arrayref(r0, i0, st), r0 -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, is_arrayref(r0, i0, st[r -- i ', val]) ∧ (0 ≤ j ∧ j < i0 → okval(st[r -- i ', val][r0 -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-92, ⊦ is_typevalue(typeval(ty))], [CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : typefuns, , ref, ⊦ ty ≤ ty], [CSIMPNAMEDSEQ : javatype, , sel-01, ⊦ mkarraytype(ty) .type = ty], [CSIMPNAMEDSEQ : javavalue, , sel-11, ⊦ typeval(ty) .type = ty], [CSIMPNAMEDSEQ : specialkeys, , len, ⊦ _length ≠ i '], [CSIMPNAMEDSEQ : refkey, , inj-01, ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPNAMEDSEQ : store, javastore, In-insert, ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : typefuns, , array, ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])]]