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 Conditional, ExprArray, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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