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Proof step 15 from proof addarray-identity (previous step)

is_fskey(sk), st[r -- _type] .type = mkarraytype(ty), is_array(r, st) ⊦ (r -- sk ∈ addarray(r, ty, getarray(r, st), st) → r -- sk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[r -- sk]) = st[r -- sk], ¬ is_indexkey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, ¬ is_fskey(sk) ∧ (¬ 0 ≤ sk .index ∨ ¬ sk .index < n→i(# getarray(r, st)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
st[r -- _type] .type = mkarraytype(ty), is_fskey(sk), is_array(r, st) ⊦ (r -- sk ∈ addarray(r, ty, getarray(r, st), st) → r -- sk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[r -- sk]) = st[r -- sk], sk ≠ _type ∧ sk ≠ _length

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])]]