Let α be given.
Assume Ha.
Let β be given.
Assume Hb.
Let γ be given.
Assume Hc.
We prove the intermediate
claim Lc:
ordinal γ.
An
exact proof term for the current goal is
ordinal_Hered α Ha γ Hc.
We prove the intermediate
claim Lab:
ordinal (α + β).
An exact proof term for the current goal is Ha.
An exact proof term for the current goal is Hb.
We prove the intermediate
claim Lcb:
ordinal (γ + β).
An exact proof term for the current goal is Lc.
An exact proof term for the current goal is Hb.
We will
prove γ + β ∈ α + β.
We will
prove γ + β < α + β.
An exact proof term for the current goal is Lc.
An exact proof term for the current goal is Hb.
An exact proof term for the current goal is Ha.
∎