Expression of type Lambda

from the theory of proveit.core_expr_types.tuples

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, Lambda, b, d
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Lambda([a_1_to_i, b, c_1_to_k, d], Conditional(Equals([a_1_to_i, b, c_1_to_k], [a_1_to_i, d, c_1_to_k]).with_wrapping_at(2), Equals(b, d)))

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_{k}, d\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i}, b,c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i}, d,c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array} \textrm{ if } b = d\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	11, 10, 13, 12
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 12
8	ExprTuple	11, 10, 13
9	ExprTuple	11, 12, 13
10	Variable
11	ExprRange	lambda_map: 14 start_index: 17 end_index: 15
12	Variable
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Lambda	parameter: 24 body: 19
15	Variable
16	Lambda	parameter: 24 body: 20
17	Literal
18	Variable
19	IndexedVar	variable: 21 index: 24
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable