Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 10
6	ExprTuple	9, 8, 11
7	ExprTuple	9, 10, 11
8	Variable
9	ExprRange	lambda_map: 12 start_index: 15 end_index: 13
10	Variable
11	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
12	Lambda	parameter: 22 body: 17
13	Variable
14	Lambda	parameter: 22 body: 18
15	Literal
16	Variable
17	IndexedVar	variable: 19 index: 22
18	IndexedVar	variable: 20 index: 22
19	Variable
20	Variable
21	ExprTuple	22
22	Variable