Expression of type ExprArray

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 A, B, ExprArray, ExprRange, IndexedVar, Variable, k, m, n
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = [sub_expr1, sub_expr2]
expr = ExprArray(ExprRange(sub_expr1, [ExprRange(sub_expr2, IndexedVar(A, sub_expr3), one, n), ExprRange(sub_expr2, IndexedVar(B, sub_expr3), one, k)], one, m).with_explicit_parameterization())

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())

\begin{array}{cccccccc} 
 A_{1, 1} & A_{1, 2} & \cdots & A_{1, n} & B_{1, 1} & B_{1, 2} & \cdots & B_{1, k} \\
A_{2, 1} & A_{2, 2} & \cdots & A_{2, n} & B_{2, 1} & B_{2, 2} & \cdots & B_{2, k} \\
\begin{array}{c}:\\ A_{{_{-}b}, 1} \\:\end{array} & \begin{array}{c}:\\ A_{{_{-}b}, 2} \\:\end{array} & \ddots & \begin{array}{c}:\\ A_{{_{-}b}, n} \\:\end{array} & \begin{array}{c}:\\ B_{{_{-}b}, 1} \\:\end{array} & \begin{array}{c}:\\ B_{{_{-}b}, 2} \\:\end{array} & \ddots & \begin{array}{c}:\\ B_{{_{-}b}, k} \\:\end{array} \\
A_{m, 1} & A_{m, 2} & \cdots & A_{m, n} & B_{m, 1} & B_{m, 2} & \cdots & B_{m, k} \\
\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	with_justification

# display the expression information
stored_expr.expr_info()

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