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, Real, RealNeg, greater, zero

# 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 = Less(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), domain = RealNeg), And(InSet(i, Natural), InSet(j, Natural), greater(Add(i, j), zero)))))

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}^-}~\left[\forall_{b \in \mathbb{R}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) < b\right)\right] \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  \left(i + j\right) > 0\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: 25 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 21 operand: 7
4	Operation	operator: 23 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9, 10
7	Lambda	parameters: 11 body: 12
8	Operation	operator: 41 operands: 13
9	Operation	operator: 41 operands: 14
10	Operation	operator: 37 operands: 15
11	ExprTuple	48, 50
12	Conditional	value: 16 condition: 17
13	ExprTuple	52, 18
14	ExprTuple	55, 18
15	ExprTuple	19, 20
16	Operation	operator: 21 operand: 26
17	Operation	operator: 23 operands: 24
18	Literal
19	Literal
20	Operation	operator: 46 operands: 25
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	ExprTuple	52, 55
26	Lambda	parameter: 49 body: 30
27	ExprRange	lambda_map: 31 start_index: 54 end_index: 52
28	ExprRange	lambda_map: 32 start_index: 54 end_index: 55
29	ExprTuple	49
30	Conditional	value: 33 condition: 34
31	Lambda	parameter: 61 body: 35
32	Lambda	parameter: 61 body: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 41 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	ExprTuple	43, 49
39	ExprTuple	49, 44
40	ExprTuple	56, 45
41	Literal
42	ExprTuple	57, 45
43	Operation	operator: 46 operands: 47
44	Literal
45	Literal
46	Literal
47	ExprTuple	48, 49, 50
48	ExprRange	lambda_map: 51 start_index: 54 end_index: 52
49	Variable
50	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
51	Lambda	parameter: 61 body: 56
52	Variable
53	Lambda	parameter: 61 body: 57
54	Literal
55	Variable
56	IndexedVar	variable: 58 index: 61
57	IndexedVar	variable: 59 index: 61
58	Variable
59	Variable
60	ExprTuple	61
61	Variable