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Proof step 89 from proof putarray-addarray-one (previous step)

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])

User applied rule cut formula

And obtained the following new goals

Proof step 60:
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])
Proof step 88:
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), (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

[fma-arg: ( r0 -- sk ∈ putArray (vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st)) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st)) ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (( r0 -- sk ∈ putArray (vals, r, 1, addarray(r, ty, n→i(# vals) + 1, st)) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st)))]]