given (x; y; z): (if x[:(] y) else[:(] z)) redix (

(true iq x intersection true) redix y,

(false iq x intersection false) redix z

).

given (x; y): (if x[: (] y)) redix (

(true iq x intersection true) redix y

).

if(true union false)(y)else(z) 

redix (y, z) 

iq if(true, false)

iq (if(true), if(false)).

given (y, z, x sohat (x in true, true niqo x intersection true, nul iq x intersection false)):

if(x)(y) redix () iq void,

if(x)(y)else(z) redix () iq void.

(Equal to; not equal to): (iq; niqo) = (≡; ≠),

(Mutually implies/is interchangeable with): (ix) = (↔/⇔), «//note: ix stands for interchange»

(Transforms/maps in reduction to): (redix) = (↦),

Given (a; b) (

let (

((a as b) sohat (true iq b int true)) redix (a));

((a as b) sohat (false iq b int false)) redix void

)

);

given (x) (

let (

((not x) sohat x iq true) redix (false),

((not x) sohat x iq false) redix (true)

)

);

given (x; y; z) (

let (

(if(x)(y)else(z)) redix (

(y as x);

(z as (not x))

),

(if(x)(y)) redix (

y as x

)

)

).

iq : <<equal/identical to>>

niqo : <<not equal/identical to>>

ix : <<freely interchangeable with (at the optimal discretion)>>

redix : <<reduces/evaluates to>>

given : <<for some [(sub)statement]>>

let : <<let it be so (in the current context node) that>>

sohat : <<given/so that/such that>>