Step
*
2
of Lemma
sys-antecedent-filter-image
.....set predicate.....
1. Info : Type
2. A : Type
3. B : Type
4. g : A ─→ bag(B)
5. es : EO+(Info)
6. X : EClass(A)
7. f : E(X) ─→ E(X)
8. ∀x:E(X). f x c≤ x
9. ∀a:E(X). ((¬((f a) = a ∈ E(X)))
⇒ (#(g X(a)) = 1 ∈ ℤ)
⇒ (#(g X(f a)) = 1 ∈ ℤ))
⊢ ∀x:E(g[X]). f x c≤ x
BY
{ (Auto THEN BackThruSomeHyp THEN DoSubsume THEN Auto THEN BLemma `es-E-filter-image` THEN Auto)⋅ }
Latex:
Latex:
.....set predicate.....
1. Info : Type
2. A : Type
3. B : Type
4. g : A {}\mrightarrow{} bag(B)
5. es : EO+(Info)
6. X : EClass(A)
7. f : E(X) {}\mrightarrow{} E(X)
8. \mforall{}x:E(X). f x c\mleq{} x
9. \mforall{}a:E(X). ((\mneg{}((f a) = a)) {}\mRightarrow{} (\#(g X(a)) = 1) {}\mRightarrow{} (\#(g X(f a)) = 1))
\mvdash{} \mforall{}x:E(g[X]). f x c\mleq{} x
By
Latex:
(Auto THEN BackThruSomeHyp THEN DoSubsume THEN Auto THEN BLemma `es-E-filter-image` THEN Auto)\mcdot{}
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