The Gauge Integral Theory in HOL4

Table 1

Some HOL4 notations and their semantics.

Meaning	HOL notations	Standard notations
Truth	𝑇	𝑇
Falsity	𝐹	⟂
Negation	~t	¬t
Disjunction	𝑡1∨𝑡2	𝑡1∨𝑡2
Conjunction	t1∧t2	𝑡1∧𝑡2
Implication	𝑡1==>𝑡2	𝑡1⇒𝑡2
Equality	𝑡1=𝑡2	𝑡1=𝑡2
∀-quantification	!𝑥 · 𝑡	∀ 𝑥⋅𝑡
∃-quantification	?𝑥 · 𝑡	∃ 𝑥⋅𝑡
Lambda	⧵𝑥 · 𝑡	𝜆𝑥⋅𝑡