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Proof step 41 from proof putByteArray-vals-addarray-01 (previous step)

0 ≤ i, i < n→i(# bytes) + j, j ≤ i, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1, 0 ≤ j + n→i(# bytes) + i1, 0 < n→i(# bytes) + j ⊦ (putArray(mkjavavalues(bytes), r, j, putArray(mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st))[r -- i ']) = (putArray(mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), r, 0, st)[r -- i ']), bytes = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)]
Proof step 40:
j ≤ i ∧ i < n→i(# mkjavavalues(bytes)) + j, 0 ≤ i, i < n→i(# bytes) + j, j ≤ i, 0 ≤ i1, 0 ≤ j, 0 ≤ n→i(# bytes) + i1, 0 ≤ j + n→i(# bytes) + i1, 0 < n→i(# bytes) + j ⊦ (mkjavavalues(bytes)[i→n(i - j)]) = (putArray(mklist(initial_value(byte_type), i→n(j)) + mkjavavalues(bytes) + mklist(initial_value(byte_type), i→n(i1)), r, 0, st)[r -- i ']), bytes = []

Rule argument

[speclemmaarg: , j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)] ,[i, st, j, r, vals] → [i, putArray (mklist(initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st), j, r, mkjavavalues(bytes)] ,F ,storearrays , ,putar-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ # mkjavavalues(bytes) = # bytes], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i, putArray (mklist (initial_value(byte_type), (i→n(i1) + # bytes) + i→n(j)), r, 0, st), j, r, mkjavavalues(bytes))]]