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Proof step 48 from proof addarray-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk]
Proof step 44:
¬ rk .ref ≠ r, st[r -- _type] .type = mkarraytype(ty), is_array(r, st) ⊦ (rk ∈ addarray(r, ty, getarray(r, st), st) → rk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[rk]) = st[rk]
Proof step 47:
rk .ref ≠ r, st[r -- _type] .type = mkarraytype(ty), is_array(r, st) ⊦ (rk ∈ addarray(r, ty, getarray(r, st), st) → rk ∈ st) ∧ st[rk] = st[rk]

Rule argument

[crewrite-arg: add-at-01 , F , [rk, st, vals, ty, r] → [rk, st, getarray(r, st), ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (rk, st, getarray(r, st), ty, r)]]