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Step * 2 1 1 of Lemma values-for-distinct-property


1. [A] : Type
2. [V] : Type
3. eq : EqDecider(A)
4. L : (A × V) List
5. ||values-for-distinct(eq;L)|| = ||remove-repeats(eq;map(λp.(fst(p));L))|| ∈ ℤ
6. i : ℕ||remove-repeats(eq;map(λp.(fst(p));L))||
7. (remove-repeats(eq;map(λp.(fst(p));L))[i] ∈ remove-repeats(eq;map(λp.(fst(p));L)))
⊢ (remove-repeats(eq;map(λp.(fst(p));L))[i] ∈ map(λp.(fst(p));L))
BY
{ (RWO "member-remove-repeats"  (-1) THEN Auto) }

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Latex:

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Latex:

1.  [A]  :  Type
2.  [V]  :  Type
3.  eq  :  EqDecider(A)
4.  L  :  (A  \mtimes{}  V)  List
5.  ||values-for-distinct(eq;L)||  =  ||remove-repeats(eq;map(\mlambda{}p.(fst(p));L))||
6.  i  :  \mBbbN{}||remove-repeats(eq;map(\mlambda{}p.(fst(p));L))||
7.  (remove-repeats(eq;map(\mlambda{}p.(fst(p));L))[i]  \mmember{}  remove-repeats(eq;map(\mlambda{}p.(fst(p));L)))
\mvdash{}  (remove-repeats(eq;map(\mlambda{}p.(fst(p));L))[i]  \mmember{}  map(\mlambda{}p.(fst(p));L))


By

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Latex:
(RWO  "member-remove-repeats"    (-1)  THEN  Auto)

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