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Proof step 10 from proof multi-isarrayref-notin (previous step)

# refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, j0 < j, 0 ≤ j0, 0 < j, ¬ j0 < 0 ∧ ¬ j ≤ j0 → r -- j0 ' ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ j ≤ j1 → r -- j1 ' ∈ st ⊦ r ∈ refs, 0 ∈ (i0 ' + ints0) .butlast, r -- j0 ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, j0 < j, 0 ≤ j0, 0 < j, r -- j0 ' ∈ st, r ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ j ≤ j1 → r -- j1 ' ∈ st ⊦ r ∈ refs, 0 ∈ (i0 ' + ints0) .butlast, r -- j0 ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]