Guaranteed Proofs Using Interval Arithmetic - LRI

Introduction Intervals Improvements Conclusion Rational intervals Proofs Elementary functions PVSContainment property and proofs◮ If x ∈ x and y ∈ y then◮ x ⋄ y ∈ x ⋄ y, where ⋄ ∈ {+, −, ×, ÷},◮ −x ∈ −x,◮ |x| ∈ |x|,◮ x n ∈ x n .◮ Let e be a real expression on variables x 1 , . . . , x m , and letx 1 , . . . , x m be interval values such that x i ∈ x i , for 1 ≤ i ≤ m,thene(x 1 , . . . , x m ) ∈ e(x 1 , . . . , x m ),where e is the interval expression corresponding to e.Marc Daumas, Guillaume Melquiond, César MuñozGuaranteed Proofs Using Interval Arithmetic