Expression of type ExprTuple

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 Conditional, ExprArray, ExprTuple, Lambda, b, d, i
from proveit.core_expr_types import a_1_to_i, c_1_to_i
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_i, d], instance_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)), InSet(i, Natural))))

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(i \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{i}, d}~\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) \textrm{ if } i \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	36, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	31, 29, 32, 30
13	Operation	operator: 25 operands: 14
14	ExprTuple	15, 16
15	Operation	operator: 25 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	ExprTuple	31, 29
21	ExprTuple	32, 30
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	ExprTuple	31
28	ExprTuple	32
29	Variable
30	Variable
31	ExprRange	lambda_map: 33 start_index: 35 end_index: 36
32	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
33	Lambda	parameter: 42 body: 37
34	Lambda	parameter: 42 body: 38
35	Literal
36	Variable
37	IndexedVar	variable: 39 index: 42
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable