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Proof step 15 from proof junkrefs-union-disjoint (previous step)

st1 .refs ∩ st .refs = ∅, r ∈ st1, is_valid_ref(str, r, st1), st1[r -- _type] .type ≤ ty, ¬ is_valid_ref(str, r, st1 ∪ st) ∨ ¬ (st1 ∪ st)[r -- _type] .type ≤ ty ⊦ r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 9:
¬ ¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, r ∈ st1, is_valid_ref(str, r, st1), st1[r -- _type] .type ≤ ty, ¬ is_valid_ref(str, r, st1 ∪ st) ∨ ¬ (st1 ∪ st)[r -- _type] .type ≤ ty ⊦ r = jvmref
Proof step 14:
¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, r ∈ st1, is_valid_ref(str, r, st1), st1[r -- _type] .type ≤ ty, ¬ is_valid_ref(str, r, st1 ∪ st) ∨ ¬ st1[r -- _type] .type ≤ ty ⊦ r = jvmref

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r -- _type, st, st1] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r -- _type, st, st1)]]