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Proof step 14 from proof okarray-putbar-same-02 (previous step)

okarray(refval(r), byte_type, st[r -- _length] .intval, st), ∀ r, st, i. okarray(refval(r), byte_type, st[r -- _length] .intval, st) → r = jvmref ∨ okarray(refval(r), byte_type, st[r -- _length] .intval, putByteArray(bytes0, r, i, st)) ⊦ r = jvmref, okarray(refval(r), byte_type, st[r -- _length] .intval, putByteArray(by ' + bytes0, r, i, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st)[r -- i ', byteval(bytes .first)])
Proof step 13:
by ' + bytes0 ≠ [], okarray(refval(r), byte_type, st[r -- _length] .intval, st), ∀ r, st, i. okarray(refval(r), byte_type, st[r -- _length] .intval, st) → r = jvmref ∨ okarray(refval(r), byte_type, st[r -- _length] .intval, putByteArray(bytes0, r, i, st)) ⊦ r = jvmref, okarray(refval(r), byte_type, st[r -- _length] .intval, putByteArray((by ' + bytes0) .rest, r, i + 1, st)[r -- i ', byteval((by ' + bytes0) .first)])

Rule argument

[speclemmaarg: , bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st) [r -- i ', byteval(bytes .first) ] ) ,[st, i, r, bytes] → [st, i, r, by ' + bytes0] ,F ,storearrays , ,putBar-rec ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPSEQ : ⊦ by ' ≠ []], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1])], [EXTRATERMS : (st, i, r, by ' + bytes0)]]