let SAS be Semi_Affine_Space; :: thesis: for b, c, o, p being Element of SAS st not o,p,c are_collinear & o,p,b are_collinear & qtrap o,p holds
ex d being Element of SAS st trap p,b,c,d,o
let b, c, o, p be Element of SAS; :: thesis: ( not o,p,c are_collinear & o,p,b are_collinear & qtrap o,p implies ex d being Element of SAS st trap p,b,c,d,o )
assume that
A1: ( not o,p,c are_collinear & o,p,b are_collinear ) and
A2: qtrap o,p ; :: thesis: ex d being Element of SAS st trap p,b,c,d,o
consider d being Element of SAS such that
A3: ( o,p,b are_collinear implies ( o,c,d are_collinear & p,c // b,d ) ) by A2;
take d ; :: thesis: trap p,b,c,d,o
thus trap p,b,c,d,o by A1, A3; :: thesis: verum