Step
*
of Lemma
bag-member-lifting-loc-2
∀[C,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ C]. ∀[as:bag(A)]. ∀[bs:bag(B)]. ∀[i:Id]. ∀[c:C].
uiff(c ↓∈ lifting-loc-2(f) i as bs;↓∃a:A. ∃b:B. (a ↓∈ as ∧ b ↓∈ bs ∧ (c = (f i a b) ∈ C)))
BY
{ ((UnivCD THENA Auto) THEN D 0 THEN Auto) }
1
1. C : Type
2. B : Type
3. A : Type
4. f : Id ─→ A ─→ B ─→ C
5. as : bag(A)
6. bs : bag(B)
7. i : Id
8. c : C
9. c ↓∈ lifting-loc-2(f) i as bs
⊢ ↓∃a:A. ∃b:B. (a ↓∈ as ∧ b ↓∈ bs ∧ (c = (f i a b) ∈ C))
2
1. C : Type
2. B : Type
3. A : Type
4. f : Id ─→ A ─→ B ─→ C
5. as : bag(A)
6. bs : bag(B)
7. i : Id
8. c : C
9. ↓∃a:A. ∃b:B. (a ↓∈ as ∧ b ↓∈ bs ∧ (c = (f i a b) ∈ C))
⊢ c ↓∈ lifting-loc-2(f) i as bs
Latex:
Latex:
\mforall{}[C,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[as:bag(A)]. \mforall{}[bs:bag(B)]. \mforall{}[i:Id]. \mforall{}[c:C].
uiff(c \mdownarrow{}\mmember{} lifting-loc-2(f) i as bs;\mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mdownarrow{}\mmember{} as \mwedge{} b \mdownarrow{}\mmember{} bs \mwedge{} (c = (f i a b))))
By
Latex:
((UnivCD THENA Auto) THEN D 0 THEN Auto)
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