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Step * of Lemma dM-dM-homs-equal

∀[I,J:fset(ℕ)]. ∀[h1,h2:dma-hom(dM(I);dM(J))].
  h1 = h2 ∈ (Point(dM(I)) ⟶ Point(dM(J))) supposing ∀i:names(I). ((h1 <i>) = (h2 <i>) ∈ Point(dM(J)))
BY
{ (Auto THEN InstLemma `dM-homs-equal` [⌜I⌝;⌜dM(J)⌝;⌜dM-deq(J)⌝;⌜h1⌝;⌜h2⌝]⋅ THEN Auto) }

1
1. I : fset(ℕ)
2. J : fset(ℕ)
3. h1 : dma-hom(dM(I);dM(J))
4. h2 : dma-hom(dM(I);dM(J))
5. ∀i:names(I). ((h1 <i>) = (h2 <i>) ∈ Point(dM(J)))
6. i : names(I)
7. (h1 <i>) = (h2 <i>) ∈ Point(dM(J))
⊢ (h1 <1-i>) = (h2 <1-i>) ∈ Point(dM(J))

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Latex:

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Latex:
\mforall{}[I,J:fset(\mBbbN{})].  \mforall{}[h1,h2:dma-hom(dM(I);dM(J))].    h1  =  h2  supposing  \mforall{}i:names(I).  ((h1  <i>)  =  (h2  <i>))


By

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Latex:
(Auto  THEN  InstLemma  `dM-homs-equal`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}dM(J)\mkleeneclose{};\mkleeneopen{}dM-deq(J)\mkleeneclose{};\mkleeneopen{}h1\mkleeneclose{};\mkleeneopen{}h2\mkleeneclose{}]\mcdot{}  THEN  Auto)

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