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Proof step 32 from proof union-addarray-rew (previous step)

newref(r0, st), newref(r0, st0) ⊦ 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))

User applied rule cut formula

And obtained the following new goals

Proof step 22:
is_fskey(sk), newref(r0, st), newref(r0, st0) ⊦ 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))
Proof step 31:
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))

Rule argument

[fma-arg: is_fskey(sk)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (is_fskey(sk))]]