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Proof step 30 from proof junkrefs-addarray (previous step)

st[r -- _type] .type ≤ ty, newref(r0, st), junkrefs(str, r ' + acc, ty, addarray(r0, ty0, vals, st)), is_array(str, r, st), ∀ str, ty, r0, ty0, vals, st. junkrefs(str, acc, ty, addarray(r0, ty0, vals, st)) ∧ newref(r0, st) → r0 = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r0 = jvmref, r = jvmref, junkrefs(str, r ' + acc, ty, st), is_array(str, r, addarray(r0, ty0, vals, st)) ∧ (addarray(r0, ty0, vals, st)[r -- _type]) .type ≤ ty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk]
Proof step 29:
(r -- _type) .ref ≠ r0, st[r -- _type] .type ≤ ty, newref(r0, st), junkrefs(str, r ' + acc, ty, addarray(r0, ty0, vals, st)), is_array(str, r, st), ∀ str, ty, r0, ty0, vals, st. junkrefs(str, acc, ty, addarray(r0, ty0, vals, st)) ∧ newref(r0, st) → r0 = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r0 = jvmref, r = jvmref, junkrefs(str, r ' + acc, ty, st), is_array(str, r, addarray(r0, ty0, vals, st)) ∧ st[r -- _type] .type ≤ ty

Rule argument

[speclemmaarg: ,rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk] ,[rk, st, vals, ty, r] → [r -- _type, st, vals, ty0, r0] ,F ,addarray , ,add-at-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ newref(r, st) → ¬ is_array(str, r, st)])], [EXTRATERMS : (r -- _type, st, vals, ty0, r0)]]