26 lines
512 B
Lean4
26 lines
512 B
Lean4
import Game.Levels.Multiplication.L05one_mul
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World "Multiplication"
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Level 6
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Title "two_mul"
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namespace MyNat
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Introduction
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"
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This level is more important than you think; it plays
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a useful role when battling a big boss later on.
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"
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LemmaDoc MyNat.two_mul as "two_mul" in "Mul" "
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`two_mul m` is the proof that `2 * m = m + m`.
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"
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/-- For any natural number $m$, we have $ 2 \times m = m+m$. -/
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Statement two_mul
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(m : ℕ): 2 * m = m + m := by
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rw [two_eq_succ_one, succ_mul, one_mul]
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rfl
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LemmaTab "Mul"
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