t:Term. Tr(NOT(t)) 
L(t) & 
Tr(t)Tr,L:(Term
Prop). RespectsNot(Tr; L) 
Prop Q == (P 
Q) & (P Q)A,B:Prop. (A B) PropA == A FalseA:Prop. (A) Prop Termt,x:Term. (t reps x) Propt:Term. s(t) Termt,r:Term. t/r Term| Some definitions of interest. | |
| RespectsNot | Def RespectsNot(Tr; L) == t:Term. Tr(NOT(t)) L(t) & Tr(t) |
| Thm* Tr,L:(TermProp). RespectsNot(Tr; L) Prop | |
| iff | Def P Q == (P Q) & (P Q) |
| Thm* A,B:Prop. (A B) Prop | |
| not | Def A == A False |
| Thm* A:Prop. (A) Prop | |
| repst | Def x reps y == x reps y Term |
| Thm* t,x:Term. (t reps x) Prop | |
| s | Def s(t) == f(t)/q(f(t)) |
| Thm* t:Term. s(t) Term | |
| subx | Def t/e == t[e/X] |
| Thm* t,r:Term. t/r Term |
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