let Al be QC-alphabet ; :: thesis: for x, y being bound_QC-variable of Al
for A being non empty set
for v being Element of Valuations_in (Al,A)
for a being Element of A st x = y holds
(v . (x | a)) . y = a
let x, y be bound_QC-variable of Al; :: thesis: for A being non empty set
for v being Element of Valuations_in (Al,A)
for a being Element of A st x = y holds
(v . (x | a)) . y = a
let A be non empty set ; :: thesis: for v being Element of Valuations_in (Al,A)
for a being Element of A st x = y holds
(v . (x | a)) . y = a
let v be Element of Valuations_in (Al,A); :: thesis: for a being Element of A st x = y holds
(v . (x | a)) . y = a
let a be Element of A; :: thesis: ( x = y implies (v . (x | a)) . y = a )
assume A1: x = y ; :: thesis: (v . (x | a)) . y = a
then y in {x} by TARSKI:def 1;
then A2: y in dom (x .--> a) ;
(x .--> a) . y = a by A1, FUNCOP_1:72;
hence (v . (x | a)) . y = a by A2, FUNCT_4:13; :: thesis: verum