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Proof step 43 from proof multi-fieldin (previous step)

true, ∀ st, ty, acc, r, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- fs ' ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st))) ⊦ fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- fs ' ∈ addmultiarrays(refs, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# refs = i→n(countrefs(i ' + ints .rest)), posints(ints), i ≤ ints .first, 0 ≤ i, 0 ≤ ints .first, ∀ st, ty, acc, r, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- fs ' ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st))) ⊦ r -- fs ' ∈ addmultiarrays(refs, i, acc, ty, ints, st) ↔ r -- fs ' ∈ st, ints = [], fs ' = _length, fs ' = _type, 0 ∈ ints .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])]]