File: Mathlib/Data/Finset/Pointwise/Interval.lean

full_name: Finset.Icc_add_Icc_subset
code: @[to_additive Icc_add_Icc_subset]
theorem Icc_mul_Icc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Icc a b * Icc c d ⊆ Icc (a * c) (b * d) 
goal: Finset.Icc a b + Finset.Icc c d ⊆ Finset.Icc (a + c) (b + d)

full_name: Finset.Icc_mul_Icc_subset'
code: @[to_additive Icc_add_Icc_subset]
theorem Icc_mul_Icc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Icc a b * Icc c d ⊆ Icc (a * c) (b * d) 
goal: Finset.Icc a b * Finset.Icc c d ⊆ Finset.Icc (a * c) (b * d)

full_name: Finset.Iic_mul_Iic_subset'
code: @[to_additive Iic_add_Iic_subset]
theorem Iic_mul_Iic_subset' [LocallyFiniteOrderBot α] (a b : α) : Iic a * Iic b ⊆ Iic (a * b) 
goal: Finset.Iic a * Finset.Iic b ⊆ Finset.Iic (a * b)

full_name: Finset.Iic_add_Iic_subset
code: @[to_additive Iic_add_Iic_subset]
theorem Iic_mul_Iic_subset' [LocallyFiniteOrderBot α] (a b : α) : Iic a * Iic b ⊆ Iic (a * b) 
goal: Finset.Iic a + Finset.Iic b ⊆ Finset.Iic (a + b)

full_name: Finset.Ici_mul_Ici_subset'
code: @[to_additive Ici_add_Ici_subset]
theorem Ici_mul_Ici_subset' [LocallyFiniteOrderTop α] (a b : α) : Ici a * Ici b ⊆ Ici (a * b) 
goal: Finset.Ici a * Finset.Ici b ⊆ Finset.Ici (a * b)

full_name: Finset.Ici_add_Ici_subset
code: @[to_additive Ici_add_Ici_subset]
theorem Ici_mul_Ici_subset' [LocallyFiniteOrderTop α] (a b : α) : Ici a * Ici b ⊆ Ici (a * b) 
goal: Finset.Ici a + Finset.Ici b ⊆ Finset.Ici (a + b)

full_name: Finset.Icc_add_Ico_subset
code: @[to_additive Icc_add_Ico_subset]
theorem Icc_mul_Ico_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Icc a b * Ico c d ⊆ Ico (a * c) (b * d) 
goal: Finset.Icc a b + Finset.Ico c d ⊆ Finset.Ico (a + c) (b + d)

full_name: Finset.Icc_mul_Ico_subset'
code: @[to_additive Icc_add_Ico_subset]
theorem Icc_mul_Ico_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Icc a b * Ico c d ⊆ Ico (a * c) (b * d) 
goal: Finset.Icc a b * Finset.Ico c d ⊆ Finset.Ico (a * c) (b * d)

full_name: Finset.Ico_add_Icc_subset
code: @[to_additive Ico_add_Icc_subset]
theorem Ico_mul_Icc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ico a b * Icc c d ⊆ Ico (a * c) (b * d) 
goal: Finset.Ico a b + Finset.Icc c d ⊆ Finset.Ico (a + c) (b + d)

full_name: Finset.Ico_mul_Icc_subset'
code: @[to_additive Ico_add_Icc_subset]
theorem Ico_mul_Icc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ico a b * Icc c d ⊆ Ico (a * c) (b * d) 
goal: Finset.Ico a b * Finset.Icc c d ⊆ Finset.Ico (a * c) (b * d)

full_name: Finset.Ioc_mul_Ico_subset'
code: @[to_additive Ioc_add_Ico_subset]
theorem Ioc_mul_Ico_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ioc a b * Ico c d ⊆ Ioo (a * c) (b * d) 
goal: Finset.Ioc a b * Finset.Ico c d ⊆ Finset.Ioo (a * c) (b * d)

full_name: Finset.Ioc_add_Ico_subset
code: @[to_additive Ioc_add_Ico_subset]
theorem Ioc_mul_Ico_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ioc a b * Ico c d ⊆ Ioo (a * c) (b * d) 
goal: Finset.Ioc a b + Finset.Ico c d ⊆ Finset.Ioo (a + c) (b + d)

full_name: Finset.Ico_mul_Ioc_subset'
code: @[to_additive Ico_add_Ioc_subset]
theorem Ico_mul_Ioc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ico a b * Ioc c d ⊆ Ioo (a * c) (b * d) 
goal: Finset.Ico a b * Finset.Ioc c d ⊆ Finset.Ioo (a * c) (b * d)

full_name: Finset.Ico_add_Ioc_subset
code: @[to_additive Ico_add_Ioc_subset]
theorem Ico_mul_Ioc_subset' [LocallyFiniteOrder α] (a b c d : α) :
    Ico a b * Ioc c d ⊆ Ioo (a * c) (b * d) 
goal: Finset.Ico a b + Finset.Ioc c d ⊆ Finset.Ioo (a + c) (b + d)

full_name: Finset.Iic_add_Iio_subset
code: @[to_additive Iic_add_Iio_subset]
theorem Iic_mul_Iio_subset' [LocallyFiniteOrderBot α] (a b : α) : Iic a * Iio b ⊆ Iio (a * b) 
goal: Finset.Iic a + Finset.Iio b ⊆ Finset.Iio (a + b)

full_name: Finset.Iic_mul_Iio_subset'
code: @[to_additive Iic_add_Iio_subset]
theorem Iic_mul_Iio_subset' [LocallyFiniteOrderBot α] (a b : α) : Iic a * Iio b ⊆ Iio (a * b) 
goal: Finset.Iic a * Finset.Iio b ⊆ Finset.Iio (a * b)

full_name: Finset.Iio_add_Iic_subset
code: @[to_additive Iio_add_Iic_subset]
theorem Iio_mul_Iic_subset' [LocallyFiniteOrderBot α] (a b : α) : Iio a * Iic b ⊆ Iio (a * b) 
goal: Finset.Iio a + Finset.Iic b ⊆ Finset.Iio (a + b)

full_name: Finset.Iio_mul_Iic_subset'
code: @[to_additive Iio_add_Iic_subset]
theorem Iio_mul_Iic_subset' [LocallyFiniteOrderBot α] (a b : α) : Iio a * Iic b ⊆ Iio (a * b) 
goal: Finset.Iio a * Finset.Iic b ⊆ Finset.Iio (a * b)

full_name: Finset.Ioi_add_Ici_subset
code: @[to_additive Ioi_add_Ici_subset]
theorem Ioi_mul_Ici_subset' [LocallyFiniteOrderTop α] (a b : α) : Ioi a * Ici b ⊆ Ioi (a * b) 
goal: Finset.Ioi a + Finset.Ici b ⊆ Finset.Ioi (a + b)

full_name: Finset.Ioi_mul_Ici_subset'
code: @[to_additive Ioi_add_Ici_subset]
theorem Ioi_mul_Ici_subset' [LocallyFiniteOrderTop α] (a b : α) : Ioi a * Ici b ⊆ Ioi (a * b) 
goal: Finset.Ioi a * Finset.Ici b ⊆ Finset.Ioi (a * b)

full_name: Finset.Ici_mul_Ioi_subset'
code: @[to_additive Ici_add_Ioi_subset]
theorem Ici_mul_Ioi_subset' [LocallyFiniteOrderTop α] (a b : α) : Ici a * Ioi b ⊆ Ioi (a * b) 
goal: Finset.Ici a * Finset.Ioi b ⊆ Finset.Ioi (a * b)

full_name: Finset.Ici_add_Ioi_subset
code: @[to_additive Ici_add_Ioi_subset]
theorem Ici_mul_Ioi_subset' [LocallyFiniteOrderTop α] (a b : α) : Ici a * Ioi b ⊆ Ioi (a * b) 
goal: Finset.Ici a + Finset.Ioi b ⊆ Finset.Ioi (a + b)