let P be pcs-Str ; :: thesis: for a being set
for p, q being Element of P
for p1, q1 being Element of (pcs-extension (P,a)) st p = p1 & q = q1 & p (--) q holds
p1 (--) q1
let a be set ; :: thesis: for p, q being Element of P
for p1, q1 being Element of (pcs-extension (P,a)) st p = p1 & q = q1 & p (--) q holds
p1 (--) q1
let p, q be Element of P; :: thesis: for p1, q1 being Element of (pcs-extension (P,a)) st p = p1 & q = q1 & p (--) q holds
p1 (--) q1
let p1, q1 be Element of (pcs-extension (P,a)); :: thesis: ( p = p1 & q = q1 & p (--) q implies p1 (--) q1 )
assume that
A1: p = p1 and
A2: q = q1 and
A3: [p,q] in the ToleranceRel of P ; :: according to PCS_0:def 7 :: thesis: p1 (--) q1
the ToleranceRel of P c= the ToleranceRel of (pcs-extension (P,a)) by Th21;
hence [p1,q1] in the ToleranceRel of (pcs-extension (P,a)) by A1, A2, A3; :: according to PCS_0:def 7 :: thesis: verum