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
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Lambda([a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j], Conditional(Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), Equals([b_1_to_j], [d_1_to_j])))

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_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array} \textrm{ if } \left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)\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	12, 14, 13, 15
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, 11
8	ExprTuple	12, 14, 13
9	ExprTuple	12, 15, 13
10	ExprTuple	14
11	ExprTuple	15
12	ExprRange	lambda_map: 16 start_index: 22 end_index: 17
13	ExprRange	lambda_map: 18 start_index: 22 end_index: 19
14	ExprRange	lambda_map: 20 start_index: 22 end_index: 23
15	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
16	Lambda	parameter: 33 body: 24
17	Variable
18	Lambda	parameter: 33 body: 25
19	Variable
20	Lambda	parameter: 33 body: 26
21	Lambda	parameter: 33 body: 27
22	Literal
23	Variable
24	IndexedVar	variable: 28 index: 33
25	IndexedVar	variable: 29 index: 33
26	IndexedVar	variable: 30 index: 33
27	IndexedVar	variable: 31 index: 33
28	Variable
29	Variable
30	Variable
31	Variable
32	ExprTuple	33
33	Variable