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Step * of Lemma agree_on_common_iseg

∀[T:Type]
  ∀as2,bs2,as1,bs1:T List.  (as1 ≤ as2 ⇒ bs1 ≤ bs2 ⇒ agree_on_common(T;as2;bs2) ⇒ agree_on_common(T;as1;bs1))
BY
{ InductionOnList }

1
1. [T] : Type
⊢ ∀bs2,as1,bs1:T List.  (as1 ≤ [] ⇒ bs1 ≤ bs2 ⇒ agree_on_common(T;[];bs2) ⇒ agree_on_common(T;as1;bs1))

2
1. [T] : Type
2. u : T
3. v : T List
4. ∀bs2,as1,bs1:T List.  (as1 ≤ v ⇒ bs1 ≤ bs2 ⇒ agree_on_common(T;v;bs2) ⇒ agree_on_common(T;as1;bs1))
⊢ ∀bs2,as1,bs1:T List.  (as1 ≤ [u / v] ⇒ bs1 ≤ bs2 ⇒ agree_on_common(T;[u / v];bs2) ⇒ agree_on_common(T;as1;bs1))

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Latex:

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Latex:
\mforall{}[T:Type]
    \mforall{}as2,bs2,as1,bs1:T  List.
        (as1  \mleq{}  as2  {}\mRightarrow{}  bs1  \mleq{}  bs2  {}\mRightarrow{}  agree\_on\_common(T;as2;bs2)  {}\mRightarrow{}  agree\_on\_common(T;as1;bs1))


By

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Latex:
InductionOnList

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