Expression of type ExprRange

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, 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 = ExprRange(sub_expr1, [ExprRange(sub_expr2, IndexedVar(A, sub_expr3), one, n), ExprRange(sub_expr2, IndexedVar(B, sub_expr3), one, k)], one, m)

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, 1}, A_{1, 2}, \ldots, A_{1, n},B_{1, 1}, B_{1, 2}, \ldots, B_{1, k}\right), \left(A_{2, 1}, A_{2, 2}, \ldots, A_{2, n},B_{2, 1}, B_{2, 2}, \ldots, B_{2, k}\right), \ldots, \left(A_{m, 1}, A_{m, 2}, \ldots, A_{m, n},B_{m, 1}, B_{m, 2}, \ldots, B_{m, k}\right)

stored_expr.style_options()

name	description	default	current value	related methods
parameterization	'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).	None	None/False	('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansion	The number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.	2	2	('with_front_expansion', 'get_front_expansion')
back_expansion	The number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.	1	1	('with_back_expansion', 'get_back_expansion')
order	The default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'	increasing	increasing	('with_decreasing_order', 'with_increasing_order')
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
case_simplify	If 'True', simplify formatted instances that are ConditionalSets under proper index assumptions	False	False	('with_case_simplification',)

# display the expression information
stored_expr.expr_info()

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