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Proof step 13 from proof addbar-refval-01 (previous step)

# ints = m + 1, i < n→i(m), 0 ≤ i, ∀ st, r, i, ints0. # ints0 < m + 1 → (0 ≤ i ∧ i < n→i(# ints0) → ints0 = [] ∨ is_bytevalue(addarray(r, byte_type, mkjavavalues(is2bs(ints0)), st)[r -- i '])) ⊦ i = n→i(m), ints = [], m = 0, is_bytevalue(addarray(r, byte_type, mkjavavalues(is2bs(ints .butlast)), st)[r -- i '])

User applied rule apply induction

And obtained the following new goals

Proof step 12:
ints .butlast = [] ∨ is_bytevalue(addarray(r, byte_type, mkjavavalues(is2bs(ints .butlast)), st)[r -- i ']), # ints = m + 1, i < n→i(m), 0 ≤ i, ∀ st, r, i, ints0. # ints0 < m + 1 → (0 ≤ i ∧ i < n→i(# ints0) → ints0 = [] ∨ is_bytevalue(addarray(r, byte_type, mkjavavalues(is2bs(ints0)), st)[r -- i '])) ⊦ i = n→i(m), ints = [], m = 0, is_bytevalue(addarray(r, byte_type, mkjavavalues(is2bs(ints .butlast)), st)[r -- i '])

Rule argument

[substlist-arg: [st, r, i, ints0] → [st, r, i, ints .butlast]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n ≤ m ↔ n = 0], [CSIMPSEQ : n0 < n ⊦ m + ((* n)) ≤ m0 + ((* n0)) ↔ m + (n - n0) ≤ m0], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ints ≠ [] → # ints .butlast = # ints - 1], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ n→i(m) < n→i(n) ↔ m < n], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (st, r, i, ints .butlast)]]