let s be SynTypes_Calculus; :: thesis: for T, X being FinSequence of s
for x, y, z being type of s st T ==>. y & X ^ <*x*> ==>. z holds
(X ^ <*(x /" y)*>) ^ T ==>. z
let T, X be FinSequence of s; :: thesis: for x, y, z being type of s st T ==>. y & X ^ <*x*> ==>. z holds
(X ^ <*(x /" y)*>) ^ T ==>. z
let x, y, z be type of s; :: thesis: ( T ==>. y & X ^ <*x*> ==>. z implies (X ^ <*(x /" y)*>) ^ T ==>. z )
assume that
A1: T ==>. y and
A2: X ^ <*x*> ==>. z ; :: thesis: (X ^ <*(x /" y)*>) ^ T ==>. z
(X ^ <*x*>) ^ H₂(s) ==>. z by A2, FINSEQ_1:34;
then ((X ^ <*(x /" y)*>) ^ T) ^ H₂(s) ==>. z by A1, Def18;
hence (X ^ <*(x /" y)*>) ^ T ==>. z by FINSEQ_1:34; :: thesis: verum