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Proof step 35 from proof addarray-identity (previous step)

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)))

User applied rule cut formula

And obtained the following new goals

Proof step 15:
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)))
Proof step 34:
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)))

Rule argument

[fma-arg: is_fskey(sk)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (is_fskey(sk))]]