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Proof step 47 from proof addarray-addaray (previous step)

¬ ( r ≠ r ∨ r = r ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# mklist(initial_value(ty), i→n(i))) ≤ sk .index)), r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st, ¬ is_indexkey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, ¬ is_fskey(sk) ∧ (¬ 0 ≤ sk .index ∨ ¬ sk .index < i)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]