Expression of type And

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, Set

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

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())

\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]

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.	()	()	('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',)

# 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: 12 operands: 20
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 17 body: 9
8	ExprTuple	17
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	17, 16
14	Literal
15	ExprTuple	17, 18
16	Variable
17	Variable
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21
21	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
22	Lambda	parameter: 28 body: 25
23	Literal
24	Variable
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable