let a, b, c, d be Real; :: thesis: ( a <= b & c <= d implies NE-corner (rectangle (a,b,c,d)) = |[b,d]| )

set K = rectangle (a,b,c,d);

assume that

A1: a <= b and

A2: c <= d ; :: thesis: NE-corner (rectangle (a,b,c,d)) = |[b,d]|

A3: NE-corner (rectangle (a,b,c,d)) = |[(E-bound (rectangle (a,b,c,d))),(N-bound (rectangle (a,b,c,d)))]| by PSCOMP_1:def 13;

E-bound (rectangle (a,b,c,d)) = b by A1, A2, Th38;

hence NE-corner (rectangle (a,b,c,d)) = |[b,d]| by A1, A2, A3, Th37; :: thesis: verum

set K = rectangle (a,b,c,d);

assume that

A1: a <= b and

A2: c <= d ; :: thesis: NE-corner (rectangle (a,b,c,d)) = |[b,d]|

A3: NE-corner (rectangle (a,b,c,d)) = |[(E-bound (rectangle (a,b,c,d))),(N-bound (rectangle (a,b,c,d)))]| by PSCOMP_1:def 13;

E-bound (rectangle (a,b,c,d)) = b by A1, A2, Th38;

hence NE-corner (rectangle (a,b,c,d)) = |[b,d]| by A1, A2, A3, Th37; :: thesis: verum