[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 55 from proof putByteArray-vals-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]
Proof step 54:
¬ n < # mkjavavalues(bytes), 0 < n→i(# bytes) + i1 + j, n→i(n) < n→i(# bytes) + i1, # bytes ≤ n, 0 < n→i(# bytes) + i1, 0 ≤ n→i(n) + j, n < i→n(i1) + # bytes, 0 ≤ j + n→i(# bytes) + i1, 0 ≤ n→i(# bytes) + i1, 0 ≤ j, 0 < i1 ⊦ initial_value(byte_type) = (mklist(initial_value(byte_type), i→n(i1))[n - # mkjavavalues(bytes)]), i1 = 0

Rule argument

[speclemmaarg: ,¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals] ,[n, vals0, vals] → [n, mklist(initial_value(byte_type), i→n(i1)), mkjavavalues(bytes)] ,F ,list-del ,javavalues ,get-append-grt ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n < # vals → (vals + vals0)[n] = vals[n]], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # mkjavavalues(bytes) = # bytes], [CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)])], [EXTRATERMS : (n, mklist(initial_value(byte_type), i→n(i1)), mkjavavalues(bytes))]]