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Proof step 45 from proof isarray-put-array-badindex (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 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 5:
⊦ oktype(val0, ty, st[r1 -- sk, val]) ↔ oktype(val0, ty, st)
Proof step 6:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 44:
st[r0 -- _type] = typeval(mkarraytype(ty)), i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ r0 = jvmref, is_typevalue(typeval(mkarraytype(ty))) ∧ is_arraytype(typeval(mkarraytype(ty)) .type) ∧ typeval(mkarraytype(ty)) .type .type ≤ ty ∧ r0 -- _length ∈ st[r -- i ', val] ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)) ↔ okarray(r0, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : javastore, , length-at, ⊦ (st[r -- i ', val] [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPNAMEDSEQ : typefuns, , array, ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPNAMEDSEQ : javastore, , type, ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])]]