Step
*
1
2
1
1
1
2
of Lemma
name-morph-decomp
.....subterm..... T:t
1:n
1. I : Cname List
2. J : Cname List
3. f : name-morph(I;J)
4. ∀[f@0:{x:nameset(I)| ↑¬bisname(f x)} ⟶ (Cname × ℕ2)]. (mapfilter(f@0;λx.(¬bisname(f x));I) ∈ (Cname × ℕ2) List)
5. mapfilter(λx.<x, f x>;λx.(¬bisname(f x));I) ∈ (Cname × ℕ2) List
6. I ∈ nameset(I) List
7. x : nameset(filter(λx.(¬bisname(f x));I) @ filter(λx.isname(f x);I))
⊢ x ∈ nameset(I)
BY
{ (D -1 THEN (RW ListC (-1) THENA Auto) THEN D -1 THEN (RW ListC (-1) THENA Auto) THEN MemTypeCD THEN Auto) }
Latex:
Latex:
.....subterm..... T:t
1:n
1. I : Cname List
2. J : Cname List
3. f : name-morph(I;J)
4. \mforall{}[f@0:\{x:nameset(I)| \muparrow{}\mneg{}\msubb{}isname(f x)\} {}\mrightarrow{} (Cname \mtimes{} \mBbbN{}2)]
(mapfilter(f@0;\mlambda{}x.(\mneg{}\msubb{}isname(f x));I) \mmember{} (Cname \mtimes{} \mBbbN{}2) List)
5. mapfilter(\mlambda{}x.<x, f x>\mlambda{}x.(\mneg{}\msubb{}isname(f x));I) \mmember{} (Cname \mtimes{} \mBbbN{}2) List
6. I \mmember{} nameset(I) List
7. x : nameset(filter(\mlambda{}x.(\mneg{}\msubb{}isname(f x));I) @ filter(\mlambda{}x.isname(f x);I))
\mvdash{} x \mmember{} nameset(I)
By
Latex:
(D -1
THEN (RW ListC (-1) THENA Auto)
THEN D -1
THEN (RW ListC (-1) THENA Auto)
THEN MemTypeCD
THEN Auto)
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