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Proof step 18 from proof putBar-lastrec (previous step)

∀ by, r, i, st. putByteArray(bytes0 + by ', r, i, st) = (putByteArray(bytes0, r, i, st)[r -- (i + n→i(# bytes0)) ', byteval(by)]) ⊦ (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- i ', byteval(by0)][r -- ((1 + n→i(# bytes0)) + i) ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 17:
r -- ((1 + n→i(# bytes0)) + i) ' ≠ r -- i ', ∀ by, r, i, st. putByteArray(bytes0 + by ', r, i, st) = (putByteArray(bytes0, r, i, st)[r -- (i + n→i(# bytes0)) ', byteval(by)]) ⊦ (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- ((1 + n→i(# bytes0)) + i) ', byteval(by)][r -- i ', byteval(by0)])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [byteval(by), r -- ((1 + n→i(# bytes0)) + i) ', byteval(by0), r -- i ', putByteArray(bytes0, r, i + 1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i = i + j ↔ j = 0], [CSIMPSEQ : ⊦ 0 ≠ n→i(m) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (byteval(by), r -- ((1 + n→i(# bytes0)) + i) ', byteval(by0), r -- i ', putByteArray(bytes0, r, i + 1, st))]]