Step
*
1
of Lemma
simple-comb1-classrel
.....antecedent.....
1. Info : Type
2. B : Type
3. C : Type
4. f : B ─→ C
5. X : EClass(B)
6. es : EO+(Info)
7. e : E
8. v : C
⊢ ∀v:C. ∀bs:k:ℕ1 ─→ bag((λn.[B][n]) k).
(v ↓∈ (λw.lifting1(f;w 0)) bs
⇐⇒ ↓∃vs:k:ℕ1 ─→ ((λn.[B][n]) k). ((∀k:ℕ1. vs k ↓∈ bs k) ∧ (v = ((λw.(f (w 0))) vs) ∈ C)))
BY
{ (UnivCD THEN Try (Complete (Auto))) }
1
1. Info : Type
2. B : Type
3. C : Type
4. f : B ─→ C
5. X : EClass(B)
6. es : EO+(Info)
7. e : E
8. v : C
9. v1 : C@i
10. bs : k:ℕ1 ─→ bag((λn.[B][n]) k)@i
⊢ v1 ↓∈ (λw.lifting1(f;w 0)) bs
⇐⇒ ↓∃vs:k:ℕ1 ─→ ((λn.[B][n]) k). ((∀k:ℕ1. vs k ↓∈ bs k) ∧ (v1 = ((λw.(f (w 0))) vs) ∈ C))
Latex:
Latex:
.....antecedent.....
1. Info : Type
2. B : Type
3. C : Type
4. f : B {}\mrightarrow{} C
5. X : EClass(B)
6. es : EO+(Info)
7. e : E
8. v : C
\mvdash{} \mforall{}v:C. \mforall{}bs:k:\mBbbN{}1 {}\mrightarrow{} bag((\mlambda{}n.[B][n]) k).
(v \mdownarrow{}\mmember{} (\mlambda{}w.lifting1(f;w 0)) bs
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}vs:k:\mBbbN{}1 {}\mrightarrow{} ((\mlambda{}n.[B][n]) k). ((\mforall{}k:\mBbbN{}1. vs k \mdownarrow{}\mmember{} bs k) \mwedge{} (v = ((\mlambda{}w.(f (w 0))) vs))))
By
Latex:
(UnivCD THEN Try (Complete (Auto)))
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