Expression of type Equals

from the theory of proveit.core_expr_types.expr_arrays

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 ExprArray, b, d
from proveit.core_expr_types import a_1_to_i, c_1_to_i
from proveit.logic import And, Equals

# build up the expression from sub-expressions
expr = Equals(Equals(ExprArray(a_1_to_i, b), ExprArray(c_1_to_i, d)), And(Equals([a_1_to_i], [c_1_to_i]), Equals(b, d))).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} \left(\left(\begin{array}{c} 
 \multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{1} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{2} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & \vdots & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{i} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & b & \rightarrow \end{array}} \\
\end{array}
\right) = \left(\begin{array}{c} 
 \multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & c_{1} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & c_{2} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & \vdots & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & c_{i} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & d & \rightarrow \end{array}} \\
\end{array}
\right)\right) =  \\ \left(\left(\left(a_{1}, a_{2}, \ldots, a_{i}\right) = \left(c_{1}, c_{2}, \ldots, c_{i}\right)\right) \land \left(b = d\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: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 12 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	ExprTuple	18, 16
8	ExprTuple	19, 17
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	ExprTuple	18
15	ExprTuple	19
16	Variable
17	Variable
18	ExprRange	lambda_map: 20 start_index: 22 end_index: 23
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
20	Lambda	parameter: 29 body: 24
21	Lambda	parameter: 29 body: 25
22	Literal
23	Variable
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable