[SR] Demonstration of simplification

Demonstration of the possible reduction from an accelerated frame of reference to a Galilean frame of reference over a very short duration or interval.
 We pose:
ΔTo²=ΔTr²+ΔEt²
ΔTo²=ΔTr²+Δx²/c²
ΔTo²=ΔTr²+(1/4)(a²/c²)(Tr2²-Tr1²)²
ΔTo²=ΔTr²+(1/4)(a²/c²)[(Tr2+Tr1)(Tr2-Tr1)]²
ΔTo²=ΔTr²+(1/4)(a²/c²)(Tr2+Tr1)².ΔTr²
ΔTo²=ΔTr²[1+(1/4)(a²/c²)(Tr2+Tr1)²]
ΔTo²=ΔTr²[1+(1/4)(a²/c²)(2Trm)²]
ΔTo²=ΔTr²[1+(a²/c²)(Trm)²]
ΔTo²=ΔTr²(1+Vri²/c²)
 Let ΔTo=ΔTr.sqrt(1+Vr²/c²)
 and Voi=Vri/sqrt(1+Vri²/c²)
 As in the Galilean frames of reference.
 Note that the instantaneous speed given for frames accelerated by physicists is not correct, and that the correct formula is simply Voi/c=(1+c²/2ax)^(-1/2)
 It's a lot less than what they say.
 R.H.