2015-11-04 21:53:12 -08:00
|
|
|
/- Basic rewriting with iff with congr_iff -/
|
|
|
|
|
import logic.connectives
|
|
|
|
|
open nat
|
2015-11-16 16:00:00 -08:00
|
|
|
|
|
|
|
|
attribute not_true [simp]
|
|
|
|
|
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 0) -- true
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 1) -- true
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 2) -- true
|
|
|
|
|
#simplify iff env 2 (@lt nat nat_has_lt 0 0) -- false
|
|
|
|
|
#simplify iff env 2 (@lt nat nat_has_lt 0 (succ 0)) -- true
|
|
|
|
|
#simplify iff env 2 (@lt nat nat_has_lt 1 (succ 1)) -- true
|
|
|
|
|
#simplify iff env 2 (@lt nat nat_has_lt 0 (succ (succ 0))) -- true
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 0) -- true
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 1) -- true
|
|
|
|
|
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @lt nat nat_has_lt 0 0) -- false
|
