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Proof step 11 from proof validref-putbar (previous step)

validref(str, r, ty, st), okreftype(refval(r0), mkarraytype(byte_type), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], byte_type, st)), r0 ∈ st, ∀ str, r, ty, st, r0, i. validref(str, r, ty, st) ∧ okbytearray(r0, st) → r = r0 ∨ validref(str, r, ty, putByteArray(bytes0, r0, i, st)) ⊦ r = r0, st[r0 -- _type] .type .type = byte_type, r0 = jvmref, validref(str, r, ty, putByteArray(bytes0, r0, i + 1, st)[r0 -- i ', byteval(by)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
validref(str, r, ty, st), okreftype(refval(r0), mkarraytype(byte_type), st), r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), r0 ∈ st, 0 ≤ st[r0 -- _length] .intval, ∀ str, r, ty, st, r0, i. validref(str, r, ty, st) ∧ okbytearray(r0, st) → r = r0 ∨ validref(str, r, ty, putByteArray(bytes0, r0, i, st)), ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → is_bytevalue(st[r0 -- j ']) ⊦ r = r0, st[r0 -- _type] .type .type = byte_type, r0 = jvmref, validref(str, r, ty, putByteArray(bytes0, r0, i + 1, st)[r0 -- i ', byteval(by)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]