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Proof step 14 from proof addarray-identity (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
st[r -- _type] .type = mkarraytype(ty), is_fskey(sk), is_array(r, st) ⊦ sk ≠ _type, (r -- sk ∈ addarray(r, ty, getarray(r, st), st) → r -- sk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[r -- sk]) = st[r -- sk]
Proof step 13:
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]

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]