Expression of type Forall

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 = Forall(instance_param_or_params = [A_1_to_m, B], instance_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())

\forall_{A_{1}, A_{2}, \ldots, A_{m}, B}~\left(\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}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 13 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 8 body: 3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 20 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	29, 24
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 20 operands: 28
12	Operation	operator: 13 operand: 15
13	Literal
14	ExprTuple	15
15	Lambda	parameter: 25 body: 17
16	ExprTuple	25
17	Conditional	value: 18 condition: 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29
29	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
30	Lambda	parameter: 36 body: 33
31	Literal
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable