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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, c, 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, Real, RealNonNeg, greater_eq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, c_1_to_j], Conditional(Forall(instance_param_or_params = [b], instance_expr = greater_eq(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonNeg), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), RealNonNeg), one, j)))))

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_{i}, c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \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) \textrm{ if } \left(a_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(a_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{R}^{\ge 0}\right), \left(c_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(c_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{R}^{\ge 0}\right)\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	32, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 33 body: 14
11	ExprRange	lambda_map: 15 start_index: 38 end_index: 36
12	ExprRange	lambda_map: 16 start_index: 38 end_index: 39
13	ExprTuple	33
14	Conditional	value: 17 condition: 18
15	Lambda	parameter: 45 body: 19
16	Lambda	parameter: 45 body: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 25 operands: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	33, 27
23	ExprTuple	33, 28
24	ExprTuple	40, 29
25	Literal
26	ExprTuple	41, 29
27	Operation	operator: 30 operands: 31
28	Literal
29	Literal
30	Literal
31	ExprTuple	32, 33, 34
32	ExprRange	lambda_map: 35 start_index: 38 end_index: 36
33	Variable
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	Lambda	parameter: 45 body: 40
36	Variable
37	Lambda	parameter: 45 body: 41
38	Literal
39	Variable
40	IndexedVar	variable: 42 index: 45
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable