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, Real, RealPos, greater, zero

# build up the expression from sub-expressions
expr = 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(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), domain = RealPos), 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 24 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 20 operand: 6
3	Operation	operator: 22 operands: 5
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 10 body: 11
7	Operation	operator: 40 operands: 12
8	Operation	operator: 40 operands: 13
9	Operation	operator: 36 operands: 14
10	ExprTuple	47, 49
11	Conditional	value: 15 condition: 16
12	ExprTuple	51, 17
13	ExprTuple	54, 17
14	ExprTuple	18, 19
15	Operation	operator: 20 operand: 25
16	Operation	operator: 22 operands: 23
17	Literal
18	Literal
19	Operation	operator: 45 operands: 24
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	51, 54
25	Lambda	parameter: 48 body: 29
26	ExprRange	lambda_map: 30 start_index: 53 end_index: 51
27	ExprRange	lambda_map: 31 start_index: 53 end_index: 54
28	ExprTuple	48
29	Conditional	value: 32 condition: 33
30	Lambda	parameter: 60 body: 34
31	Lambda	parameter: 60 body: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 40 operands: 38
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	ExprTuple	48, 42
38	ExprTuple	48, 43
39	ExprTuple	55, 44
40	Literal
41	ExprTuple	56, 44
42	Operation	operator: 45 operands: 46
43	Literal
44	Literal
45	Literal
46	ExprTuple	47, 48, 49
47	ExprRange	lambda_map: 50 start_index: 53 end_index: 51
48	Variable
49	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
50	Lambda	parameter: 60 body: 55
51	Variable
52	Lambda	parameter: 60 body: 56
53	Literal
54	Variable
55	IndexedVar	variable: 57 index: 60
56	IndexedVar	variable: 58 index: 60
57	Variable
58	Variable
59	ExprTuple	60
60	Variable