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, Natural, Real, RealNonNeg, greater_eq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, c_1_to_j], instance_expr = Forall(instance_param_or_params = [b], instance_expr = greater_eq(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), domain = RealNonNeg), 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}, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}^{\ge 0}}~\left[\forall_{b \in \mathbb{R}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \geq b\right)\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	48, 51
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operand: 8
5	Operation	operator: 20 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 37 operands: 13
10	Operation	operator: 37 operands: 14
11	ExprTuple	44, 46
12	Conditional	value: 15 condition: 16
13	ExprTuple	48, 17
14	ExprTuple	51, 17
15	Operation	operator: 18 operand: 22
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Lambda	parameter: 45 body: 26
23	ExprRange	lambda_map: 27 start_index: 50 end_index: 48
24	ExprRange	lambda_map: 28 start_index: 50 end_index: 51
25	ExprTuple	45
26	Conditional	value: 29 condition: 30
27	Lambda	parameter: 57 body: 31
28	Lambda	parameter: 57 body: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 37 operands: 35
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	ExprTuple	45, 39
35	ExprTuple	45, 40
36	ExprTuple	52, 41
37	Literal
38	ExprTuple	53, 41
39	Operation	operator: 42 operands: 43
40	Literal
41	Literal
42	Literal
43	ExprTuple	44, 45, 46
44	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
45	Variable
46	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
47	Lambda	parameter: 57 body: 52
48	Variable
49	Lambda	parameter: 57 body: 53
50	Literal
51	Variable
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable