Expression of type Lambda

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, Lambda, 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 = Lambda([a_1_to_i, b, c_1_to_i, d], 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())

\left(a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{i}, d\right) \mapsto \left(\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}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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