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Proof step 13 from proof addarray-identity (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ r -- _length ∈ addarray(r0, ty, vals, st) ↔ r = r0 ∨ r -- _length ∈ st
Proof step 10:
⊦ (addarray(r, ty, vals, st)[r -- _length]) = intval(n→i(# vals))
Proof step 12:
st[r -- _type] .type = mkarraytype(ty), is_array(r, st), r -- _length ∈ st, r ∈ st ⊦ intval(n→i(# getarray(r, st))) = st[r -- _length]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ r -- _length ∈ st → ¬ is_array(r, st)], [CSIMPSEQ : ⊦ is_fskey(_length)])]]