Expression of type And

from the theory of proveit.logic.booleans.disjunction

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 A, B, C, ExprRange, IndexedVar, Variable, m, n
from proveit.logic import And, Boolean, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), InSet(B, Boolean), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n), B)

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())

\left(A_{1} \in \mathbb{B}\right) \land  \left(A_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(A_{m} \in \mathbb{B}\right) \land \left(B \in \mathbb{B}\right)\land \left(C_{1} \in \mathbb{B}\right) \land  \left(C_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(C_{n} \in \mathbb{B}\right) \land B

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, 5, 13
3	ExprRange	lambda_map: 6 start_index: 10 end_index: 7
4	Operation	operator: 16 operands: 8
5	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
6	Lambda	parameter: 24 body: 12
7	Variable
8	ExprTuple	13, 20
9	Lambda	parameter: 24 body: 14
10	Literal
11	Variable
12	Operation	operator: 16 operands: 15
13	Variable
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 20
16	Literal
17	ExprTuple	19, 20
18	IndexedVar	variable: 21 index: 24
19	IndexedVar	variable: 22 index: 24
20	Literal
21	Variable
22	Variable
23	ExprTuple	24
24	Variable