2015-11-05 05:53:12 +00:00
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/- Basic rewriting with iff with congr_iff -/
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import logic.connectives
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open nat
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2015-11-17 00:00:00 +00:00
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attribute not_true [simp]
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#simplify iff env 2 (@le nat nat_has_le 0 0) -- true
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#simplify iff env 2 (@le nat nat_has_le 0 1) -- true
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#simplify iff env 2 (@le nat nat_has_le 0 2) -- true
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#simplify iff env 2 (@lt nat nat_has_lt 0 0) -- false
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#simplify iff env 2 (@lt nat nat_has_lt 0 (succ 0)) -- true
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#simplify iff env 2 (@lt nat nat_has_lt 1 (succ 1)) -- true
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#simplify iff env 2 (@lt nat nat_has_lt 0 (succ (succ 0))) -- true
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#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 0) -- true
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#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 1) -- true
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#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @lt nat nat_has_lt 0 0) -- false
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