---

Step * of Lemma equiv_rel_subtyping

∀[T:Type]. ∀[R:T ⟶ T ⟶ Type]. ∀[Q:T ⟶ ℙ].  (EquivRel(T;x,y.R[x;y]) ⇒ EquivRel({z:T| Q[z]} ;x,y.R[x;y]))
BY
{ (Auto THEN (Assert ⌜{z:T| Q[z]}  ⊆r T⌝⋅ THEN Auto) THEN FLemma `equiv_rel_subtype` [-1;-2] THEN Auto) }

---

Latex:

---

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  Type].  \mforall{}[Q:T  {}\mrightarrow{}  \mBbbP{}].    (EquivRel(T;x,y.R[x;y])  {}\mRightarrow{}  EquivRel(\{z:T|  Q[z]\}  ;x,y.R\000C[x;y]))


By

---

Latex:
(Auto
  THEN  (Assert  \mkleeneopen{}\{z:T|  Q[z]\}    \msubseteq{}r  T\mkleeneclose{}\mcdot{}  THEN  Auto)
  THEN  FLemma  `equiv\_rel\_subtype`  [-1;-2]
  THEN  Auto)

---

Home Index