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Proof step 69 from proof union-addarray-rew (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 54:
is_fskey(sk), newref(r0, st), newref(r0, st0), is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ⊦ r0 = jvmref, (r0 -- sk ∈ addarray(r0, ty, vals, st0) → r0 -- sk ∈ st ∨ r0 -- sk ∈ st0) ∧ (st ∪ st0)[r0 -- sk] = (st ∪ addarray(r0, ty, vals, st0))[r0 -- sk]
Proof step 68:
newref(r0, st), newref(r0, st0), is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ⊦ is_fskey(sk), r0 = jvmref, (r0 -- sk ∈ addarray(r0, ty, vals, st0) → r0 -- sk ∈ st ∨ r0 -- sk ∈ st0) ∧ (st ∪ st0)[r0 -- sk] = (st ∪ addarray(r0, ty, vals, st0))[r0 -- sk]

Rule argument

[fma-arg: is_fskey(sk)]

Additional information

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