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Proof step 12 from proof putbytearray-addarray-override (previous step)

# 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 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ # vals ≤ n → (vals + vals0)[n, val] = vals + vals0[n - # vals, val]
Proof step 11:
# vals0 ≤ # vals0, # 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 - # vals0, byteval(by)], st)) = addarray(r, byte_type, vals0 + byteval(by) ' + mkjavavalues(bytes0), st), vals1 = []

Rule argument

[speclemmaarg: ,# vals ≤ n → (vals + vals0)[n, val] = vals + vals0[n - # vals, val] ,[val, n, vals0, vals] → [byteval(by), # vals0, vals1, vals0] ,F ,list-del ,javavalues ,put-app-right ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (byteval(by), # vals0, vals1, vals0)]]