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Proof step 15 from proof getbar-onlyModified-all (previous step)

0 ≤ j, 0 ≤ i, onlyModified(str, r, st, st0), okbytearray(r1, st), okbytearray(r, st), ∀ i, st0, str, r1, st, r, j0. i→n(j0) < i→n(j) → ( okbytearray(r, st) ∧ okbytearray(r1, st) ∧ onlyModified(str, r, st, st0) ∧ 0 ≤ i ∧ 0 ≤ j0 → getbytearray(r1, i, j0, st) = getbytearray(r1, i, j0, st0) ∨ r = r1) ⊦ r = r1, getbytearray(r1, i, j, st) = getbytearray(r1, i, j, st0)

User applied rule induction

And obtained the following new goals

Proof step 14:
0 ≤ j ∧ 0 ≤ i ∧ onlyModified(str, r, st, st0) ∧ okbytearray(r1, st) ∧ okbytearray(r, st) ∧ (∀ i, st0, str, r1, st, r, j0. i→n(j0) < i→n(j) → ( okbytearray(r, st) ∧ okbytearray(r1, st) ∧ onlyModified(str, r, st, st0) ∧ 0 ≤ i ∧ 0 ≤ j0 → getbytearray(r1, i, j0, st) = getbytearray(r1, i, j0, st0) ∨ r = r1)), ∀ r1, st0, st, r, str, i, j0. i→n(j0) < i→n(j) → ( 0 ≤ j0 ∧ 0 ≤ i ∧ onlyModified(str, r, st, st0) ∧ okbytearray(r1, st) ∧ okbytearray(r, st) ∧ (∀ i, st0, str, r1, st, r, j1. i→n(j1) < i→n(j0) → ( okbytearray(r, st) ∧ okbytearray(r1, st) ∧ onlyModified(str, r, st, st0) ∧ 0 ≤ i ∧ 0 ≤ j1 → getbytearray(r1, i, j1, st) = getbytearray(r1, i, j1, st0) ∨ r = r1)) → r = r1 ∨ getbytearray(r1, i, j0, st) = getbytearray(r1, i, j0, st0)) ⊦ r = r1 ∨ getbytearray(r1, i, j, st) = getbytearray(r1, i, j, st0)

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, i→n(j), [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (i→n(j))]]