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Proof step 20 from proof okarray-byte-01 (previous step)

st[r -- (i0 + i) '] = byteval(st[r0 -- (j0 + i) '] .byteval), 0 ≤ j0 + i, 0 ≤ i0 + i, r0 ∈ st, r ∈ st, j0 + j < st[r0 -- _length] .intval, i0 + j < st[r -- _length] .intval, i < j, 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)), okarray(r, byte_type, st) ⊦ is_bytevalue(st[r0 -- (j0 + i) ']), r0 = jvmref, r = jvmref, byteval(st[r0 -- (j0 + i) '] .byteval) = st[r0 -- (j0 + i) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ 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 14:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 19:
st[r -- (i0 + i) '] = byteval(st[r0 -- (j0 + i) '] .byteval), st[r0 -- _type] .type = mkarraytype(byte_type), r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), okarray(r, byte_type, st), 0 ≤ j0 + i, 0 ≤ i0 + i, r ∈ st, j0 + j < st[r0 -- _length] .intval, i0 + j < st[r -- _length] .intval, i < j, r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), 0 ≤ st[r0 -- _length] .intval, r0 ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j1 → is_bytevalue(st[r0 -- j1 ']) ⊦ r = jvmref, byteval(st[r0 -- (j0 + i) '] .byteval) = st[r0 -- (j0 + i) '], r0 = jvmref, is_bytevalue(st[r0 -- (j0 + i) '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]