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Proof step 31 from proof union-addarray-rew (previous step)

newref(r0, st), newref(r0, st0) ⊦ is_fskey(sk), r0 = jvmref, (r0 -- sk ∈ addarray(r0, ty, vals, st ∪ st0) ↔ r0 -- sk ∈ st ∨ r0 -- sk ∈ addarray(r0, ty, vals, st0)) ∧ (addarray(r0, ty, vals, st ∪ st0)[r0 -- sk]) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- sk], ¬ is_indexkey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, ¬ is_fskey(sk) ∧ (¬ 0 ≤ sk .index ∨ ¬ sk .index < n→i(# vals))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
0 ≤ sk .index, sk .index < n→i(# vals), is_indexkey(sk), newref(r0, st0), newref(r0, st) ⊦ r0 = jvmref, vals = [], (r0 -- sk ∈ addarray(r0, ty, vals, st ∪ st0) ↔ r0 -- sk ∈ st ∨ r0 -- sk ∈ addarray(r0, ty, vals, st0)) ∧ (addarray(r0, ty, vals, st ∪ st0)[r0 -- sk]) = (st ∪ addarray(r0, ty, vals, st0))[r0 -- sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]