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Proof step 21 from proof validref-putbar (previous step)

validref(str, r, ty, st), okbytearray(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, validref(str, r, ty, putByteArray(by ' + bytes0, r0, i, 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 20:
by ' + bytes0 ≠ [], validref(str, r, ty, st), okbytearray(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, validref(str, r, ty, putByteArray((by ' + bytes0) .rest, r0, i + 1, st)[r0 -- 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, r0, 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, r0, by ' + bytes0)]]