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18 lines
689 B
Idris
18 lines
689 B
Idris
nat_induction :
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(prop : Nat -> Type) -> -- Property to show
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(prop Z) -> -- Base case
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((k : Nat) -> prop k -> prop (S k)) -> -- Inductive step
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(x : Nat) -> -- Show for all x
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prop x
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nat_induction prop p_Z p_S Z = p_Z
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nat_induction prop p_Z p_S (S k) = p_S k (nat_induction prop p_Z p_S k)
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plus_ind : Nat -> Nat -> Nat
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plus_ind n m
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= nat_induction (\x => Nat)
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m -- Base case, plus_ind Z m
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(\k, k_rec => S k_rec) -- Inductive step plus_ind (S k) m
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-- where k_rec = plus_ind k m
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n
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