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Proof step 18 from proof getbytearray-subset (previous step)

st ⊆ st0, 0 ≤ i, ∀ j0. ¬ j0 < 0 ∧ ¬ i + j ≤ j0 → r -- j0 ' ∈ st ⊦ # getbytearray(r, i, j, st) = # getbytearray(r, i, j, st0) ∧ (n < # getbytearray(r, i, j, st) → (getbytearray(r, i, j, st)[n]) = (getbytearray(r, i, j, st0)[n]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ j → # getbytearray(r, i, j, st) = i→n(j)
Proof step 4:
⊦ j < 0 → getbytearray(r, i, j, st) = []
Proof step 17:
0 ≤ j, st ⊆ st0, 0 ≤ i, ∀ j0. ¬ j0 < 0 ∧ ¬ i + j ≤ j0 → r -- j0 ' ∈ st ⊦ i→n(j) = # getbytearray(r, i, j, st0) ∧ (n < i→n(j) → (getbytearray(r, i, j, st)[n]) = (getbytearray(r, i, j, st0)[n]))

Rule argument

[crewrite-arg: bar-len-02, F, [st, j, i, r] → [st, j, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ ¬ n < 0])], [EXTRATERMS : (st, j, i, r)]]