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Proof step 12 from proof addarray-mode (previous step)

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

User applied rule apply induction

And obtained the following new goals

Proof step 11:
# vals = m + 1, _mode ∈ (addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)]), ∀ st, ty, r, vals0. # vals0 < m + 1 → (_mode ∈ addarray(r, ty, vals0, st) → r = jvmref ∨ _mode ∈ st) ⊦ _mode ∈ addarray(r, ty, vals .butlast, st), vals = [], r = jvmref, _mode ∈ st

Rule argument

[substlist-arg: [st, ty, r, vals0] → [st, ty, r, vals .butlast]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals ≠ [] → # vals .butlast = # vals - 1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : n0 < n ⊦ m + ((* n)) ≤ m0 + ((* n0)) ↔ m + (n - n0) ≤ m0], [CSIMPSEQ : ⊦ m + m0 ≤ m ↔ m0 = 0])], [EXTRATERMS : (st, ty, r, vals .butlast)]]