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Proof step 52 from proof putarray-addarray-one (previous step)

r0 -- sk ∈ addarray(r0, ty, n→i(# vals) + 1, st) ∨ ¬ is_fskey(sk) ∧ ¬ sk .index ≤ 0 ∧ ¬ n→i(# vals) < sk .index ↔ r0 -- sk ∈ addarray(r0, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ (putArray(vals, r0, 1, addarray(r0, ty, n→i(# vals) + 1, st))[r0 -- sk]) = (addarray(r0, ty, refval(jvmref) ' + vals, st)[r0 -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_fskey(sk) → (putArray(vals, r, i, st)[r -- sk]) = st[r -- sk]
Proof step 37:
¬ is_fskey(sk), r0 -- sk ∈ addarray(r0, ty, n→i(# vals) + 1, st) ∨ ¬ is_fskey(sk) ∧ ¬ sk .index ≤ 0 ∧ ¬ n→i(# vals) < sk .index ↔ r0 -- sk ∈ addarray(r0, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ (putArray(vals, r0, 1, addarray(r0, ty, n→i(# vals) + 1, st))[r0 -- sk]) = (addarray(r0, ty, refval(jvmref) ' + vals, st)[r0 -- sk])
Proof step 51:
is_fskey(sk), r0 -- sk ∈ addarray(r0, ty, n→i(# vals) + 1, st) ∨ ¬ is_fskey(sk) ∧ ¬ sk .index ≤ 0 ∧ ¬ n→i(# vals) < sk .index ↔ r0 -- sk ∈ addarray(r0, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ (addarray(r0, ty, n→i(# vals) + 1, st)[r0 -- sk]) = (addarray(r0, ty, refval(jvmref) ' + vals, st)[r0 -- sk])

Rule argument

[speclemmaarg: ,is_fskey(sk) → (putArray(vals, r, i, st)[r -- sk]) = st[r -- sk] ,[sk, st, i, r, vals] → [sk, addarray(r0, ty, n→i(# vals) + 1, st), 1, r0, vals] ,F ,storearrays , ,putArray-at ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk, addarray(r0, ty, n→i(# vals) + 1, st), 1, r0, vals)]]