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Proof step 14 from proof subset-size (previous step)

st1[rk] = (st0 -- (r -- sk))[rk], # st0 .refs < # st1 .refs, r ∈ st1 .refs, r ∈ st0 .refs, r ∈ st0, r -- sk ∈ st0, rk ∈ st1, rk ∈ st0, ∀ rk0. rk0 ∈ st1 → rk0 ∈ st0 ∧ st1[rk0] = (st0 -- (r -- sk))[rk0], ∀ st. # st1 .refs ≤ # st .refs ∨ ¬ st1 ⊆ st ⊦ st0 = ∅, st1 = ∅, st1[rk] = st0[rk], r -- sk ∈ st1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st -- rk0)[rk] = st[rk] ,[rk, rk0, st] → [rk, r -- sk, st0] ,F ,store ,javastore ,Del-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ (st -- rk)[rk] = ∅[rk]])], [EXTRATERMS : (rk, r -- sk, st0)]]