[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 3 from proof copy-between (previous step)

j0 < i0 + j, i0 ≤ j0, 0 < j, ∀ j1, r, r0, i0, j0, i, st. i→n(j1) < i→n(j) → (true → (r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r -- ((j0 - i0) + i) '])) ⊦ (arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = st[r -- (i + j0 - i0) '], r = r0, i0 + j = j0 + 1

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [j1, r, r0, i0, j0, i, st] → [j - 1, r, r0, i0, j0, i, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ i ≠ i0 → (¬ i < i0 ↔ i0 < i)], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRATERMS : (j - 1, r, r0, i0, j0, i, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])]]