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Proof step 18 from proof subset-size (previous step)

st1[a, d] ⊆ st0, # st0 ≤ # st1, ∀ st0. # st0 < # st1 → ¬ st1 ⊆ st0 ⊦ st1[a, d] = ∅, a ∈ st1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ st[a, d] ⊆ st0 ↔ st -- a ⊆ st0 -- a ∧ a × d ∈ st0
Proof step 20:
st1 -- a ⊆ st0 -- a ∧ a × d ∈ st0, # st0 ≤ # st1, ∀ st0. # st0 < # st1 → ¬ st1 ⊆ st0 ⊦ st1[a, d] = ∅, a ∈ st1

Rule argument

spec: store inst: name: subset-put-02 seq: ⊦ st[a, d] ⊆ st0 ↔ st -- a ⊆ st0 -- a ∧ a × d ∈ st0 subst: [st0, d, a, st] → [st0, d, a, st1] flags: rewrite, current

Additional information

Used terms: st0, d, a, st1