Expression of type ExprTuple

from the theory of proveit.core_expr_types.conditionals

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, ConditionalSet, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, c, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import Equals, FALSE
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_m, b, c_1_to_n], Equals(ConditionalSet(ExprRange(sub_expr1, Conditional(IndexedVar(a, sub_expr1), FALSE), one, m), b, ExprRange(sub_expr1, Conditional(IndexedVar(c, sub_expr1), FALSE), one, n)), b)))

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(a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}\right) \mapsto \left(\left\{\begin{array}{ccc}a_{1} \textrm{ if } \bot \\ a_{2} \textrm{ if } \bot \\  \vdots \\ a_{m} \textrm{ if } \bot \\ b \\ c_{1} \textrm{ if } \bot \\ c_{2} \textrm{ if } \bot \\  \vdots \\ c_{n} \textrm{ if } \bot\end{array}\right.. = b\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	4, 14, 5
3	Operation	operator: 6 operands: 7
4	ExprRange	lambda_map: 8 start_index: 19 end_index: 17
5	ExprRange	lambda_map: 9 start_index: 19 end_index: 20
6	Literal
7	ExprTuple	10, 14
8	Lambda	parameter: 29 body: 23
9	Lambda	parameter: 29 body: 24
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14, 15
13	ExprRange	lambda_map: 16 start_index: 19 end_index: 17
14	Variable
15	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
16	Lambda	parameter: 29 body: 21
17	Variable
18	Lambda	parameter: 29 body: 22
19	Literal
20	Variable
21	Conditional	value: 23 condition: 25
22	Conditional	value: 24 condition: 25
23	IndexedVar	variable: 26 index: 29
24	IndexedVar	variable: 27 index: 29
25	Literal
26	Variable
27	Variable
28	ExprTuple	29
29	Variable