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Proof step 36 from proof okbytearray-put-byteval-equiv (previous step)

okreftype(refval(r), mkarraytype(byte_type), st[r -- i ', byteval(by)]) ∧ r ≠ jvmref ∧ r -- _length ∈ st[r -- i ', byteval(by)] ∧ is_integervalue(st[r -- i ', byteval(by)][r -- _length]) ∧ 0 ≤ (st[r -- i ', byteval(by)][r -- _length]) .intval ∧ is_arrayref(r, (st[r -- i ', byteval(by)][r -- _length]) .intval, st[r -- i ', byteval(by)]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r -- i ', byteval(by)][r -- _length]) .intval → oktype(st[r -- i ', byteval(by)][r -- j '], byte_type, st[r -- i ', byteval(by)])), i < 0 ∨ st[r -- _length] .intval ≤ i ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']) ⊦ r = jvmref, okbytearray(r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 35:
st[r -- _type] .type = mkarraytype(byte_type), r -- _type ∈ st, is_typevalue(st[r -- _type]), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st[r -- i ', byteval(by)]), r ∈ st, 0 ≤ st[r -- _length] .intval, i < 0 ∨ st[r -- _length] .intval ≤ i ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']), ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']) ⊦ r = jvmref, okbytearray(r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _length] ) = st[r0 -- _length]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _type]) = st[r0 -- _type]], [CSIMPSEQ : ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]