Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	40, 43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 27 body: 11
9	Operation	operator: 45 operands: 12
10	Operation	operator: 45 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	40, 16
13	ExprTuple	43, 16
14	Operation	operator: 45 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24, 25
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprRange	lambda_map: 28 start_index: 42 end_index: 40
23	Operation	operator: 45 operands: 29
24	ExprRange	lambda_map: 30 start_index: 42 end_index: 43
25	Operation	operator: 31 operands: 32
26	Literal
27	ExprTuple	33, 37, 34
28	Lambda	parameter: 53 body: 35
29	ExprTuple	37, 49
30	Lambda	parameter: 53 body: 36
31	Literal
32	ExprTuple	37, 38
33	ExprRange	lambda_map: 39 start_index: 42 end_index: 40
34	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
35	Operation	operator: 45 operands: 44
36	Operation	operator: 45 operands: 46
37	Variable
38	Literal
39	Lambda	parameter: 53 body: 47
40	Variable
41	Lambda	parameter: 53 body: 48
42	Literal
43	Variable
44	ExprTuple	47, 49
45	Literal
46	ExprTuple	48, 49
47	IndexedVar	variable: 50 index: 53
48	IndexedVar	variable: 51 index: 53
49	Literal
50	Variable
51	Variable
52	ExprTuple	53
53	Variable