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Proof step 9 from proof cyclic-putbar (previous step)

okbytearray(r1, st), ∀ r1, st, str, r, i. okbytearray(r1, st) → (cyclic(str, r, putByteArray(bytes0, r1, i, st)) ↔ cyclic(str, r, st)) ⊦ cyclic(str, r, putByteArray(by ' + bytes0, r1, i, st)) ↔ cyclic(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st)[r -- i ', byteval(bytes .first)])
Proof step 8:
by ' + bytes0 ≠ [], okbytearray(r1, st), ∀ r1, st, str, r, i. okbytearray(r1, st) → (cyclic(str, r, putByteArray(bytes0, r1, i, st)) ↔ cyclic(str, r, st)) ⊦ cyclic(str, r, putByteArray((by ' + bytes0) .rest, r1, i + 1, st)[r1 -- i ', byteval((by ' + bytes0) .first)]) ↔ cyclic(str, r, st)

Rule argument

[x0lemmaarg: spec-name: storearrays instance-name: lemma-name: putBar-rec antecedent: succedent: bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st) [r -- i ', byteval(bytes .first) ] ) substlist: [st, i, r, bytes] → [st, i, r1, by ' + bytes0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0, 1, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, bytelist, app-02-ant, ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPNAMEDSEQ : list, bytelist, e, ⊦ by ' ≠ []], [CSIMPNAMEDSEQ : list, bytelist, a, ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1])], [EXTRATERMS : (st, i, r1, by ' + bytes0)]]