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int_equality: rule.
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integer_equality_natural_number: rule.
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integer_intro_addition: rule.
integer_intro_subtraction: rule.
integer_intro_multiplication: rule.
integer_intro_division: rule.
integer_intro_modulo: rule.
integer_equality_addition: rule.
integer_equality_subtraction: rule.
integer_equality_multiplication: rule.
integer_equality_division: rule.
integer_equality_modulo: rule.
 integer_elim(hyp y z): int 
  tok 
  tok 
  rule.
 integer_equality_induction(over_id over u v):
tok 
  term 
  tok 
  tok 
  rule.
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int_less_equality: rule.
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where kind should be one of `UP`, `BASE` or `DOWN`.
 int_eq_computation(where): int 
  rule.
 int_less_computation(where): int 
  rule.