Step
*
of Lemma
first-eclass-val
∀[Info,A:Type].
∀Xs:EClass(A) List. ∀es:EO+(Info). ∀e:E.
(∃X∈Xs. (↑e ∈b X) ∧ (first-eclass(Xs)(e) = X(e) ∈ A)) supposing ↑e ∈b first-eclass(Xs)
BY
{ (InductionOnList THEN Auto THEN DupHyp (-1) THEN (RWW "in-first-eclass l_exists_cons" (-1) THENA Auto)) }
1
1. [Info] : Type
2. [A] : Type
3. es : EO+(Info)@i'
4. e : E@i
5. ↑e ∈b first-eclass([])
6. ↑e ∈b first-eclass([])
⊢ (∃X∈[]. (↑e ∈b X) ∧ (first-eclass([])(e) = X(e) ∈ A))
2
1. [Info] : Type
2. [A] : Type
3. u : EClass(A)@i'
4. v : EClass(A) List@i'
5. ∀es:EO+(Info). ∀e:E. (∃X∈v. (↑e ∈b X) ∧ (first-eclass(v)(e) = X(e) ∈ A)) supposing ↑e ∈b first-eclass(v)@i'
6. es : EO+(Info)@i'
7. e : E@i
8. ↑e ∈b first-eclass([u / v])
9. (↑e ∈b u) ∨ (∃X∈v. ↑e ∈b X)
⊢ (∃X∈[u / v]. (↑e ∈b X) ∧ (first-eclass([u / v])(e) = X(e) ∈ A))
Latex:
Latex:
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}X\mmember{}Xs. (\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (first-eclass(Xs)(e) = X(e))) supposing \muparrow{}e \mmember{}\msubb{} first-eclass(Xs)
By
Latex:
(InductionOnList
THEN Auto
THEN DupHyp (-1)
THEN (RWW "in-first-eclass l\_exists\_cons" (-1) THENA Auto))
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