17 lines
No EOL
405 B
Text
17 lines
No EOL
405 B
Text
import tactic
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using Nat
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rewrite_set basic
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add_rewrite add_zerol add_succl eq_id : basic
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theorem add_assoc (a b c : Nat) : a + (b + c) = (a + b) + c
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:= induction_on a
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(show 0 + (b + c) = (0 + b) + c, by simp basic)
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(λ (n : Nat) (iH : n + (b + c) = (n + b) + c),
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show (n + 1) + (b + c) = ((n + 1) + b) + c, by simp basic)
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check add_zerol
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check add_succl
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check @eq_id
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print environment 1 |