Hypergendered Logic Source

Hypergendered Logic — Page 35

HGL Source Framework · Page 35 of 293 · Source: Hypergendered Logic

Proposition 9 — SF2 inherits SF1 
By definition, 
SF2 = IH(SF1) AND IH(NOT SM1) AND PH(SF1) AND NOT PH(SM1) AND UD(SF1) AND PA(x) AND 
PA(NOT y) AND NOT FD(SF1) 
Conjunction elimination gives IHSF1, and projection gives SF1. Hence 
SF2⇒SF1. 
Proposition 10 — SF2 excludes SM1 
The same definition gives 
SF2⇒IH¬SM1. 
Projection yields 
SF2⇒¬SM1. 
This conclusion no longer depends on any provisional whole-state antithesis bridge. 
Proposition 11 — The Stage-2 male mirror 
Symmetrically, 
SM2⇒SM1 
and 
SM2⇒¬SF1. 
Proposition 12 — Higher female stages imply their immediate predecessor 
For 
, 
𝑛≥2
SF^(n+1) = IH(SF^n) AND IH(NOT SM^n) AND PH(SF^n) AND NOT PH(SM^n) AND UD(SF^n) AND NOT 
FD(SF^n), for n >= 2 
Conjunction elimination and IH projection yield 
SFn+1⇒SFn. 
Proposition 13 — Higher male stages imply their immediate predecessor 
By the mirror definition, 
SMn+1⇒SMn. 
Proposition 14 — Cumulative nesting theorem 
Repeatedly applying Propositions 12 and 13 gives 
SFn⇒HFk ∀1≤k<n, 
SMn⇒HMk ∀1≤k<n. 
This is a strict theorem of the new recursion.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:35.