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Proof step 54 from proof subset-size (previous step)

st1[r -- sk, val] ⊆ st0, # st0 .refs ≤ # st1 .refs, ∀ st. # st1 .refs ≤ # st .refs ∨ ¬ st1 ⊆ st ⊦ r ∈ st1 .refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ st[rk, val] ⊆ st0 ↔ st -- rk ⊆ st0 -- rk ∧ rk × val ∈ st0
Proof step 53:
st1 -- (r -- sk) ⊆ st0 -- (r -- sk) ∧ (r -- sk) × val ∈ st0, # st0 .refs ≤ # st1 .refs, ∀ st. # st1 .refs ≤ # st .refs ∨ ¬ st1 ⊆ st ⊦ r ∈ st1 .refs

Rule argument

[speclemmaarg: ,st[rk, val] ⊆ st0 ↔ st -- rk ⊆ st0 -- rk ∧ rk × val ∈ st0 ,[st0, val, rk, st] → [st0, val, r -- sk, st1] ,F ,store ,javastore ,subset-put-02 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, val, r -- sk, st1)]]