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