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Proof step 8 from proof union-move-left (previous step)

a ∈ st1 ⊦ a0 ∈ st0[a, st1[a]] ∪ (st1 -- a) ↔ a0 ∈ st0 ∪ st1, a0 = a, a ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ a ∈ st0 ∪ st1 ↔ a ∈ st0 ∨ a ∈ st1
Proof step 10:
a ∈ st1 ⊦ a0 ∈ st0[a, st1[a]] ∪ (st1 -- a) ↔ a0 ∈ st0 ∨ a0 ∈ st1, a0 = a, a ∈ st0

Rule argument

spec: <toplevel> name: union-in seq: ⊦ a ∈ st0 ∪ st1 ↔ a ∈ st0 ∨ a ∈ st1 subst: [st1, st0, a] → [st1, st0, a0] flags: <all paths>

Additional information

Used terms: st1, st0, a0