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Step * of Lemma Cramers-rule

∀[r:CRng]. ∀[n:ℕ]. ∀[A:Matrix(n;n;r)]. ∀[c:{c:|r|| (c * |A|) = 1 ∈ |r|} ]. ∀[b:Column(n;r)].
  ((A*c*matrix(|matrix(if y=j then b[x,0] else A[x,y])|)) = b ∈ Column(n;r))
BY
{ (Auto
   THEN DVar `c'
   THEN (InstLemma `adj-solution-property` [⌜r⌝;⌜n⌝;⌜1⌝;⌜A⌝;⌜c⌝;⌜b⌝]⋅ THENA Auto)
   THEN RWO  "adj-solution-column" (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[r:CRng].  \mforall{}[n:\mBbbN{}].  \mforall{}[A:Matrix(n;n;r)].  \mforall{}[c:\{c:|r||  (c  *  |A|)  =  1\}  ].  \mforall{}[b:Column(n;r)].
    ((A*c*matrix(|matrix(if  y=j  then  b[x,0]  else  A[x,y])|))  =  b)


By

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Latex:
(Auto
  THEN  DVar  `c'
  THEN  (InstLemma  `adj-solution-property`  [\mkleeneopen{}r\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}1\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RWO    "adj-solution-column"  (-1)
  THEN  Auto)

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