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Proof step 3 from proof disjoint-move-left (previous step)

st0 ⊥ st1 ⊦ st0[a, d] ⊥ st1 -- a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ st0 ⊥ st1 ↔ (∀ a. ¬ a ∈ st0 ∨ ¬ a ∈ st1)
Proof step 5:
st0 ⊥ st1 ⊦ ∀ a0. ¬ a0 ∈ st0[a, d] ∨ ¬ a0 ∈ st1 -- a

Rule argument

spec: <toplevel> name: disjoint seq: ⊦ st0 ⊥ st1 ↔ (∀ a. ¬ a ∈ st0 ∨ ¬ a ∈ st1) subst: [st1, st0] → [st1 -- a, st0[a, d]] flags: <all paths>

Additional information

Used terms: st1 -- a, st0[a, d]