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Commit 2017-09-16 02:55 fe1ad4b0

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feat(data/rat): derive properties of rat floor and ceil

Estimated changes

added theorem int.le_to_nat
added theorem int.lt_succ_self
added theorem int.pred_self_lt
added theorem int.to_nat_eq_max
added theorem int.to_nat_le
added theorem rat.ceil_add_int
added theorem rat.ceil_coe
added theorem rat.ceil_le
added theorem rat.ceil_mono
added theorem rat.ceil_sub_int
modified theorem rat.coe_int_add
modified theorem rat.coe_int_eq_mk
added theorem rat.coe_int_inj
added theorem rat.coe_int_le
added theorem rat.coe_int_lt
added theorem rat.coe_int_mul
added theorem rat.coe_int_neg
modified theorem rat.coe_int_one
modified theorem rat.coe_int_sub
modified theorem rat.coe_nat_rat_eq_mk
added theorem rat.floor_add_int
added theorem rat.floor_coe
added theorem rat.floor_le
added theorem rat.floor_lt
added theorem rat.floor_mono
added theorem rat.floor_sub_int
added theorem rat.le_ceil
added theorem rat.le_floor
added theorem rat.le_nat_ceil
added theorem rat.lt_nat_ceil
added theorem rat.lt_succ_floor
added theorem rat.mk_le
modified def rat.nat_ceil
added theorem rat.nat_ceil_add_nat
deleted theorem rat.nat_ceil_add_one_eq
added theorem rat.nat_ceil_coe
added theorem rat.nat_ceil_le
modified theorem rat.nat_ceil_lt_add_one
deleted theorem rat.nat_ceil_min
modified theorem rat.nat_ceil_mono
deleted theorem rat.nat_ceil_spec
modified theorem rat.nat_ceil_zero
added theorem rat.sub_def