let s be SynTypes_Calculus; :: thesis: for T, Y being FinSequence of the carrier of s
for y, x, z being type of s st T ==>. y & <*x*> ^ Y ==>. z holds
(T ^ <*(y \ x)*>) ^ Y ==>. z
let T, Y be FinSequence of the carrier of s; :: thesis: for y, x, z being type of s st T ==>. y & <*x*> ^ Y ==>. z holds
(T ^ <*(y \ x)*>) ^ Y ==>. z
let y, x, z be type of s; :: thesis: ( T ==>. y & <*x*> ^ Y ==>. z implies (T ^ <*(y \ x)*>) ^ Y ==>. z )
assume ( T ==>. y & <*x*> ^ Y ==>. z ) ; :: thesis: (T ^ <*(y \ x)*>) ^ Y ==>. z
then ( T ==>. y & (H₂(s) ^ <*x*>) ^ Y ==>. z ) by FINSEQ_1:47;
then ((H₂(s) ^ T) ^ <*(y \ x)*>) ^ Y ==>. z by Def19;
hence (T ^ <*(y \ x)*>) ^ Y ==>. z by FINSEQ_1:47; :: thesis: verum