37 lines
568 B
Lean4
37 lines
568 B
Lean4
import Game.Levels.AdvMultiplication.Level_2
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World "AdvMultiplication"
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Level 3
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Title "mul_eq_zero_iff"
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open MyNat
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Introduction
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"
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Now you have `eq_zero_or_eq_zero_of_mul_eq_zero` this is pretty straightforward.
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"
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/-- $ab = 0$, if and only if at least one of $a$ or $b$ is equal to zero.
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-/
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Statement
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{a b : ℕ} : a * b = 0 ↔ a = 0 ∨ b = 0 := by
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constructor
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intro h
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exact eq_zero_or_eq_zero_of_mul_eq_zero a b h
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intro hab
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rcases hab with hab | hab
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rw [hab]
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rw [MyNat.zero_mul]
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rfl
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rw [hab]
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rw [MyNat.mul_zero]
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rfl
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Conclusion
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"
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"
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