Source/Packages

Std.Natural

packages/foundation/standard/src/Std/Natural.alpha

325 lines48 declarations14.4 KiBSHA-256 4234d9ebfedf

def · lines 142–168

naturalDivisionStep

Full file
142def naturalDivisionStep =
143  (lambda unrestricted divisor : Nat .
144    (lambda unrestricted state : (family NaturalDivisionState) .
145      (eliminate
146        NaturalDivisionState
147        (lambda unrestricted current : (family NaturalDivisionState) .
148          (family NaturalDivisionState))
149        state
150        (branch
151          NaturalDivisionStateValue
152          remainder
153          quotient
154          .
155          (app
156            (lambda unrestricted incremented : Nat .
157              (nat-eliminate
158                (lambda unrestricted condition : Nat . (family NaturalDivisionState))
159                (constructor NaturalDivisionState NaturalDivisionStateValue incremented quotient)
160                (lambda unrestricted predecessor : Nat .
161                  (lambda unrestricted induction : (family NaturalDivisionState) .
162                    (constructor
163                      NaturalDivisionState
164                      NaturalDivisionStateValue
165                      zero
166                      (succ quotient))))
167                (naturalEqual incremented divisor)))
168            (succ remainder))))))

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