29 lines
919 B
Lean4
29 lines
919 B
Lean4
import GameServer.Commands
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import Game.Levels.LessOrEqual.L01le_refl
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import Game.Levels.LessOrEqual.L02zero_le
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import Game.Levels.LessOrEqual.L03le_succ_self
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import Game.Levels.LessOrEqual.L04le_trans
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import Game.Levels.LessOrEqual.L05le_zero
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import Game.Levels.LessOrEqual.L06le_antisymm
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import Game.Levels.LessOrEqual.L07or_symm
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import Game.Levels.LessOrEqual.L08le_total
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import Game.Levels.LessOrEqual.L09succ_le_succ
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import Game.Levels.LessOrEqual.L10le_one
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import Game.Levels.LessOrEqual.L11le_two
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World "LessOrEqual"
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Title "≤ World"
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Introduction
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"
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In this world we define `a ≤ b` and prove standard facts
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about it, such as \"if `a ≤ b` and `b ≤ c` then `a ≤ c`.\"
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The definition of `a ≤ b` is \"there exists a number `c`
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such that `b = a + c`. \" So we're going to have to learn
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a tactic to prove \"exists\" theorems, and another one
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to use \"exists\" hypotheses.
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Click on \"Start\" to proceed.
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"
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