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Proof step 5 from proof pubBar-init (previous step)

∀ class, r, i, st. initdone(class, putByteArray(bytes0, r, i, st)) ↔ initdone(class, st) ⊦ initdone(class, putByteArray(by ' + bytes0, r, i, st)) ↔ initdone(class, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st)[r -- i ', byteval(bytes .first)])
Proof step 4:
by ' + bytes0 ≠ [], ∀ class, r, i, st. initdone(class, putByteArray(bytes0, r, i, st)) ↔ initdone(class, st) ⊦ initdone(class, putByteArray((by ' + bytes0) .rest, r, i + 1, st)[r -- i ', byteval((by ' + bytes0) .first)]) ↔ initdone(class, st)

Rule argument

[crewrite-arg: putBar-rec , F , [st, i, r, bytes] → [st, i, r, by ' + bytes0] ]

Additional information

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