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Proof step 16 from proof junkref-addarray-04 (previous step)

vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, 0 ≤ i, i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), validref(str, r0, ty, st), ¬ (addarray(r, ty, vals, st)[r0 -- _type]) .type ≤ ty ∨ junkref(str, r0, addarray(r, ty, vals, st)) ⊦ r0 = jvmref, r = jvmref, ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, vals = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ newref(r, st) ∧ r0 ∈ st → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 11:
⊦ ¬ r ∈ st ∧ r ≠ jvmref → ¬ validref(str, r, ty, st)
Proof step 15:
newref(r, st) ∧ r0 ∈ st, vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, 0 ≤ i, i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), validref(str, r0, ty, st), ¬ st[r0 -- _type] .type ≤ ty ∨ junkref(str, r0, addarray(r, ty, vals, st)) ⊦ r0 = jvmref, r = jvmref, ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, vals = []

Rule argument

[speclemmaarg: , newref(r, st) ∧ r0 ∈ st → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk] ,[sk, r0, st, vals, ty, r] → [_type, r0, st, vals, ty, r] ,F ,addarray , ,addarray-at-newref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (_type, r0, st, vals, ty, r)]]