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Proof step 13 from proof putbytearray-addarray-override (previous step)

0 ≤ n→i(# vals0) ∧ i→n(n→i(# vals0)) < # (vals0 + vals1), # vals1 = 1 + # bytes0, ∀ vals, vals2, r0, st0. # vals2 = # bytes0 → putByteArray(bytes0, r0, n→i(# vals), addarray(r0, byte_type, vals + vals2, st0)) = addarray(r0, byte_type, vals + mkjavavalues(bytes0), st0) ⊦ putByteArray(bytes0, r, n→i(# vals0) + 1, addarray(r, byte_type, (vals0 + vals1)[i→n(n→i(# vals0)), byteval(by)], st)) = addarray(r, byte_type, vals0 + byteval(by) ' + mkjavavalues(bytes0), st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# vals1 = 1 + # bytes0, ∀ vals, vals2, r0, st0. # vals2 = # bytes0 → putByteArray(bytes0, r0, n→i(# vals), addarray(r0, byte_type, vals + vals2, st0)) = addarray(r0, byte_type, vals + mkjavavalues(bytes0), st0) ⊦ putByteArray(bytes0, r, n→i(# vals0) + 1, addarray(r, byte_type, (vals0 + vals1)[# vals0, byteval(by)], st)) = addarray(r, byte_type, vals0 + byteval(by) ' + mkjavavalues(bytes0), st), vals1 = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i→n(n→i(n)) = n])]]