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Proof step 34 from proof addarray-identity (previous step)

st[r -- _type] .type = mkarraytype(ty), is_array(r, st) ⊦ is_fskey(sk), (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 33:
st[r -- _type] .type = mkarraytype(ty), 0 ≤ sk .index, sk .index < n→i(# getarray(r, st)), is_indexkey(sk), is_array(r, st) ⊦ getarray(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]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]