Cryptic people

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Across
  1. 4. Singer sees line rearranged before precious stone( 4,7)
Down
  1. 1. Mate comes before spiky leaves (5,5)
  2. 2. Batman, he could be the first man to go to the Americas (4,4)
  3. 3. Singer shines a beam on prince (3,7)
  4. 5. First light on Diderot's tongue (4,6)