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Step * of Lemma inject-compose

∀[T:Type]. ∀[f,g:T ⟶ T].  (Inj(T;T;f o g)) supposing (Inj(T;T;g) and Inj(T;T;f))
BY
{ (Auto THEN InstLemma `compose-injections` [⌜T⌝;⌜f⌝;⌜g⌝]⋅ THEN Auto) }

1
1. T : Type
2. f : T ⟶ T
3. g : T ⟶ T
4. Inj(T;T;f)
5. Inj(T;T;g)
6. f o g ∈ {f:T ⟶ T| Inj(T;T;f)} 
⊢ Inj(T;T;f o g)

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[f,g:T  {}\mrightarrow{}  T].    (Inj(T;T;f  o  g))  supposing  (Inj(T;T;g)  and  Inj(T;T;f))


By

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Latex:
(Auto  THEN  InstLemma  `compose-injections`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}g\mkleeneclose{}]\mcdot{}  THEN  Auto)

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