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Proof step 14 from proof addarray-mode (previous step)

_mode ∈ (addarray(r, ty, vals .butlast, st)[r -- n→i(# vals - 1) ', vals .last][r -- _length, intval(n→i(# vals))]), ∀ st, ty, r, vals0. # vals0 < # vals → (_mode ∈ addarray(r, ty, vals0, st) → r = jvmref ∨ _mode ∈ st) ⊦ r = jvmref, vals = [], _mode ∈ st

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# vals = m + 1 ∧ # vals ≠ 0, _mode ∈ (addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(# vals))]), ∀ st, ty, r, vals0. # vals0 < # vals → (_mode ∈ addarray(r, ty, vals0, st) → r = jvmref ∨ _mode ∈ st) ⊦ r = jvmref, vals = [], _mode ∈ st

Rule argument

[speclemmaarg: n ≠ 0 ,m = n - 1 ↔ n = m + 1 ,[n, m] → [# vals, m] ,T ,nat , ,elim-pred-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (# vals, m)]]