User Manual of the RODIN Platform

(f ✁− . . . ✁− {E ↦→ F })(E) == F
E ∈ {F } == E = F where F is a single expression
(S × {F })(x) == F where F is a single expression
{E} = {F } == E = F where E and F are single expressions
{x ↦→ a, . . . , y ↦→ b} −1 == {a ↦→ x, . . . , b ↦→ y}
Ty = ∅ == ⊥
∅ = Ty == ⊥
t ∈ Ty == ⊤
In the three previous rewrite rules, Ty denotes a type expression, that is either a basic type (Z, BOOL,
any carrier set), or P(type expression), or type expression×type expression, or type expression↔type
expression, and t denotes an expression of type Ty.
U \ U \ S == S
S ∪ . . . ∪ U ∪ . . . ∪ T == U
S ∩ . . . ∩ U ∩ . . . ∩ T == S ∩ . . . ∩ T
S \ U == ∅
In the four previous rules, S and T are supposed to be of type P(U) (U thus takes the rôle of a universal
set for S and T ).
r ; ∅ == ∅
∅ ; r == ∅
f(f −1 (E)) == E
f −1 (f(E)) == E
S ⊆ A ∪ . . . ∪ S ∪ . . . ∪ B == ⊤
A ∩ . . . ∩ S ∩ . . . ∩ B ⊆ S == ⊤
A ∪ . . . ∪ B ⊆ S == A ⊆ S ∧ . . . ∧ B ⊆ S
S ⊆ A ∩ . . . ∩ B == S ⊆ A ∧ . . . ∧ S ⊆ B
A ∪ . . . ∪ B ⊂ S == A ⊂ S ∧ . . . ∧ B ⊂ S
S ⊂ A ∩ . . . ∩ B == S ⊂ A ∧ . . . ∧ S ⊂ B
A \ B ⊆ S == A ⊆ B ∪ S
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