let A be Euclidean preIfWhileAlgebra; :: thesis: for X being non empty countable set
for T being Subset of (Funcs (X,INT))
for f being Euclidean ExecutionFunction of A, Funcs (X,INT),T
for x being Variable of f
for s being Element of Funcs (X,INT) holds (. x) . s = s . x
let X be non empty countable set ; :: thesis: for T being Subset of (Funcs (X,INT))
for f being Euclidean ExecutionFunction of A, Funcs (X,INT),T
for x being Variable of f
for s being Element of Funcs (X,INT) holds (. x) . s = s . x
let T be Subset of (Funcs (X,INT)); :: thesis: for f being Euclidean ExecutionFunction of A, Funcs (X,INT),T
for x being Variable of f
for s being Element of Funcs (X,INT) holds (. x) . s = s . x
let f be Euclidean ExecutionFunction of A, Funcs (X,INT),T; :: thesis: for x being Variable of f
for s being Element of Funcs (X,INT) holds (. x) . s = s . x
let x be Variable of f; :: thesis: for s being Element of Funcs (X,INT) holds (. x) . s = s . x
let s be Element of Funcs (X,INT); :: thesis: (. x) . s = s . x
thus (. x) . s = s . ((x ^ (A,f)) . s) by Def19
.= s . x ; :: thesis: verum