13 lines
681 B
Text
13 lines
681 B
Text
/- Basic rewriting with iff with congr_iff -/
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import logic.connectives
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open nat
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#simplify iff 2 (@le nat nat_has_le 0 0) -- true
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#simplify iff 2 (@le nat nat_has_le 0 1) -- true
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#simplify iff 2 (@le nat nat_has_le 0 2) -- true
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#simplify iff 2 (@lt nat nat_has_lt 0 0) -- false
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#simplify iff 2 (@lt nat nat_has_lt 0 (succ 0)) -- true
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#simplify iff 2 (@lt nat nat_has_lt 1 (succ 1)) -- true
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#simplify iff 2 (@lt nat nat_has_lt 0 (succ (succ 0))) -- true
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#simplify iff 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 0) -- true
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#simplify iff 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 1) -- true
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#simplify iff 2 (@le nat nat_has_le 0 0 ↔ @lt nat nat_has_lt 0 0) -- false
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