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Step * of Lemma fiber-comp-exists

No Annotations
∀X:j⊢. ∀T,A:{X ⊢ _}. ∀w:{X ⊢ _:(T ⟶ A)}. ∀a:{X ⊢ _:A}.  (X ⊢ CompOp(T) ⇒ X ⊢ CompOp(A) ⇒ X ⊢ CompOp(Fiber(w;a)))
BY
{ (Auto
   THEN RenameVar `cT' (-2)
   THEN (InstLemma `composition-op-implies-composition-structure` [⌜X⌝;⌜T⌝;⌜cT⌝]⋅ THENA Auto)
   THEN RenameVar `csT' (-1)
   THEN RenameVar `cA' (-2)
   THEN (InstLemma `composition-op-implies-composition-structure` [⌜parm{i|j}⌝;⌜parm{i}⌝;⌜X⌝;⌜A⌝;⌜cA⌝]⋅ THENA Auto)
   THEN RenameVar `csA' (-1)
   THEN (BLemma `composition-structure-implies-composition-op` THENA Auto)
   THEN UseWitness ⌜fiber-comp(X;T;A;w;a;csT;csA)⌝⋅
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}X:j\mvdash{}.  \mforall{}T,A:\{X  \mvdash{}  \_\}.  \mforall{}w:\{X  \mvdash{}  \_:(T  {}\mrightarrow{}  A)\}.  \mforall{}a:\{X  \mvdash{}  \_:A\}.
    (X  \mvdash{}  CompOp(T)  {}\mRightarrow{}  X  \mvdash{}  CompOp(A)  {}\mRightarrow{}  X  \mvdash{}  CompOp(Fiber(w;a)))


By

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Latex:
(Auto
  THEN  RenameVar  `cT'  (-2)
  THEN  (InstLemma  `composition-op-implies-composition-structure`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}cT\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RenameVar  `csT'  (-1)
  THEN  RenameVar  `cA'  (-2)
  THEN  (InstLemma  `composition-op-implies-composition-structure`  [\mkleeneopen{}parm\{i|j\}\mkleeneclose{};\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}cA\mkleeneclose{}]
              \mcdot{}
              THENA  Auto
              )
  THEN  RenameVar  `csA'  (-1)
  THEN  (BLemma  `composition-structure-implies-composition-op`  THENA  Auto)
  THEN  UseWitness  \mkleeneopen{}fiber-comp(X;T;A;w;a;csT;csA)\mkleeneclose{}\mcdot{}
  THEN  Auto)

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