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Proof step 21 from proof in-add (previous step)

⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ ¬ j < 0 ∧ ¬ n→i(# vals) ≤ j ∨ r -- j ' ∈ st

User applied rule induction

And obtained the following new goals

Proof step 20:
true, ∀ st, ty, j, r, vals0. # vals0 < # vals → (true → (r -- j ' ∈ addarray(r, ty, vals0, st) ↔ ¬ j < 0 ∧ ¬ n→i(# vals0) ≤ j ∨ r -- j ' ∈ st)) ⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ ¬ j < 0 ∧ ¬ n→i(# vals) ≤ j ∨ r -- j ' ∈ st

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # vals, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# vals)]]