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Proof step 3 from proof copy-init-01 (previous step)

0 < j, ∀ j0, class1, r, i, r0, i0, st. i→n(j0) < i→n(j) → (true → (initundone(class1, arraycopy(r, i, r0, i0, j0, st)) ↔ initundone(class1, st))) ⊦ initundone(class1, arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])) ↔ initundone(class1, st)

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [j0, class1, r, i, r0, i0, st] → [j - 1, class1, r, i, r0, i0, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ initundone (class1, st[r -- i ', val]) ↔ initundone(class1, st)], [CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (j - 1, class1, r, i, r0, i0, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])]]