Expression of type ExprTuple

from the theory of proveit.numbers.addition

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, ExprTuple, Lambda, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Less, Natural, RationalNeg, RationalNonPos, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = InSet(Add(a_1_to_i, b, c_1_to_j), RationalNeg), domain = RationalNonPos, condition = Less(b, zero)), And(InSet(i, Natural), InSet(j, Natural)))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{Q}^{\leq 0}~|~b < 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{Q}^-\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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	41, 44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 19 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 28 body: 12
10	Operation	operator: 46 operands: 13
11	Operation	operator: 46 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	41, 17
14	ExprTuple	44, 17
15	Operation	operator: 46 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25, 26
21	Operation	operator: 27 operands: 28
22	Literal
23	ExprRange	lambda_map: 29 start_index: 43 end_index: 41
24	Operation	operator: 46 operands: 30
25	ExprRange	lambda_map: 31 start_index: 43 end_index: 44
26	Operation	operator: 32 operands: 33
27	Literal
28	ExprTuple	34, 38, 35
29	Lambda	parameter: 54 body: 36
30	ExprTuple	38, 50
31	Lambda	parameter: 54 body: 37
32	Literal
33	ExprTuple	38, 39
34	ExprRange	lambda_map: 40 start_index: 43 end_index: 41
35	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
36	Operation	operator: 46 operands: 45
37	Operation	operator: 46 operands: 47
38	Variable
39	Literal
40	Lambda	parameter: 54 body: 48
41	Variable
42	Lambda	parameter: 54 body: 49
43	Literal
44	Variable
45	ExprTuple	48, 50
46	Literal
47	ExprTuple	49, 50
48	IndexedVar	variable: 51 index: 54
49	IndexedVar	variable: 52 index: 54
50	Literal
51	Variable
52	Variable
53	ExprTuple	54
54	Variable