Expression of type Iff

from the theory of proveit.logic.sets.disjointness

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import B, X
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Disjoint, Forall, Iff, Set

# build up the expression from sub-expressions
expr = Iff(Disjoint(A_1_to_m, B), And(Disjoint(A_1_to_m), Forall(instance_param_or_params = [X], instance_expr = Disjoint(X, B), domain = Set(A_1_to_m)))).with_wrapping_at(2)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{c} \begin{array}{l} \textrm{disjoint}\left(A_{1}, A_{2}, \ldots, A_{m}, B\right) \Leftrightarrow  \\ \left(\textrm{disjoint}\left(A_{1}, A_{2}, \ldots, A_{m}\right) \land \left[\forall_{X \in \left\{A_{1}, A_{2}, \ldots, A_{m}\right\}}~\textrm{disjoint}\left(X, B\right)\right]\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	26, 21
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 17 operands: 25
9	Operation	operator: 10 operand: 12
10	Literal
11	ExprTuple	12
12	Lambda	parameter: 22 body: 14
13	ExprTuple	22
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Variable
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26
26	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
27	Lambda	parameter: 33 body: 30
28	Literal
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable