The initial member: Bφ ∈ P (issue #12, the mathematical starting gate)

The only point where HasWellOrderedChains enters the consistency-property construction: the base diagram itself is a member. The proof exposes the intended normalization —

• finite remainder: Bφ \ Bφ = ∅;
• remainder support and realization: vacuous;
• marking enumeration: Fin 0;
• for each α < ω₁, the source chain is requested at γ = α + 1;
• lt_gamma is discharged by α < α + 1;
• every mark and gap field reduces from the empty domain.

This separately certifies that the strengthened terminal/bottom-margin invariant (D6 and the lt_gamma addition) has not accidentally strengthened the theorem's hypothesis: an (α+1)-chain per level — exactly Marker's hypothesis, off by the harmless successor — is all that is consumed.

theorem FirstOrder.Language.baseDiagram_mem {L : Language} {φ : L.Sentenceω} {lt : L.Relations 2} (h : HasWellOrderedChains φ lt) : WOMem φ lt (baseDiagram φ lt)

The initial member: the base diagram satisfies the member predicate, from HasWellOrderedChains alone.