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Proof step 60 from proof putarray-addarray-one (previous step)

r0 -- sk ∈ putArray(vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st)) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ (r0 -- sk ∈ putArray(vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st)) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st)) ∧ (putArray(vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st))[r0 -- sk]) = (addarray(r, ty, refval(jvmref) ' + vals, st)[r0 -- sk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
r0 -- sk ∈ addarray(r, ty, n→i(# vals) + 1, st) ∨ r0 = r ∧ ¬ is_fskey(sk) ∧ ¬ sk .index ≤ 0 ∧ ¬ n→i(# vals) < sk .index ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ (r0 -- sk ∈ putArray(vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st)) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st)) ∧ (putArray(vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st))[r0 -- sk]) = (addarray(r, ty, refval(jvmref) ' + vals, st)[r0 -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 1 ≤ i ↔ 0 < i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ (r -- sk) .key = sk], [CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ rk ∈ putArray(vals, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals)])]]