Theory "marker"

Parents bool

Signature

Type	Arity
label	0
Constant	Type
:-	:label -> bool -> bool
AC	:bool reln
Abbrev	:bool -> bool
Cong	:bool -> bool
IfCases	:bool
stmarker	:α -> α
unint	:α -> α

Definitions

stmarker_def

|- ∀x. stmarker x = x

unint_def

|- ∀x. unint x = x

Abbrev_def

|- ∀x. Abbrev x ⇔ x

IfCases_def

|- IfCases ⇔ T

AC_DEF

|- ∀b1 b2. AC b1 b2 ⇔ b1 ∧ b2

Cong_def

|- ∀x. Cong x ⇔ x

label_def

|- ∀lab argument. (lab :- argument) ⇔ argument

Theorems

move_left_conj

|- ∀p q m.
     (p ∧ stmarker m ⇔ stmarker m ∧ p) ∧
     ((stmarker m ∧ p) ∧ q ⇔ stmarker m ∧ p ∧ q) ∧
     (p ∧ stmarker m ∧ q ⇔ stmarker m ∧ p ∧ q)

move_right_conj

|- ∀p q m.
     (stmarker m ∧ p ⇔ p ∧ stmarker m) ∧
     (p ∧ q ∧ stmarker m ⇔ (p ∧ q) ∧ stmarker m) ∧
     ((p ∧ stmarker m) ∧ q ⇔ (p ∧ q) ∧ stmarker m)

move_left_disj

|- ∀p q m.
     (p ∨ stmarker m ⇔ stmarker m ∨ p) ∧
     ((stmarker m ∨ p) ∨ q ⇔ stmarker m ∨ p ∨ q) ∧
     (p ∨ stmarker m ∨ q ⇔ stmarker m ∨ p ∨ q)

move_right_disj

|- ∀p q m.
     (stmarker m ∨ p ⇔ p ∨ stmarker m) ∧
     (p ∨ q ∨ stmarker m ⇔ (p ∨ q) ∨ stmarker m) ∧
     ((p ∨ stmarker m) ∨ q ⇔ (p ∨ q) ∨ stmarker m)