Expression of type Conditional

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, ExprRange, IndexedVar, Variable, VertExprArray, a, b, i
from proveit.core_expr_types import a_1_to_i, b_1_to_i
from proveit.logic import And, Equals
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(VertExprArray(a_1_to_i), VertExprArray(b_1_to_i)), And(ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), IndexedVar(b, sub_expr1)), one, i)))

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\{\left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{i} \\ \downarrow \end{array}$} \\
\end{array}
\right) = \left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{i} \\ \downarrow \end{array}$} \\
\end{array}
\right) \textrm{ if } \left(a_{1} = b_{1}\right) \land  \left(a_{2} = b_{2}\right) \land  \ldots \land  \left(a_{i} = b_{i}\right)\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: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8
6	ExprTuple	9
7	ExprTuple	10
8	ExprRange	lambda_map: 11 start_index: 14 end_index: 15
9	ExprRange	lambda_map: 12 start_index: 14 end_index: 15
10	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
11	Lambda	parameter: 24 body: 16
12	Lambda	parameter: 24 body: 19
13	Lambda	parameter: 24 body: 20
14	Literal
15	Variable
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	IndexedVar	variable: 21 index: 24
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable