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
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import InSet
from proveit.numbers import Add, Real, greater_eq

# build up the expression from sub-expressions
expr = Lambda(b, Conditional(greater_eq(Add(a_1_to_i, b, c_1_to_j), b), InSet(b, Real)))

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())

b \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \geq b \textrm{ if } b \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 14 body: 2
1	ExprTuple	14
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	14, 9
7	Literal
8	ExprTuple	14, 10
9	Operation	operator: 11 operands: 12
10	Literal
11	Literal
12	ExprTuple	13, 14, 15
13	ExprRange	lambda_map: 16 start_index: 19 end_index: 17
14	Variable
15	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
16	Lambda	parameter: 26 body: 21
17	Variable
18	Lambda	parameter: 26 body: 22
19	Literal
20	Variable
21	IndexedVar	variable: 23 index: 26
22	IndexedVar	variable: 24 index: 26
23	Variable
24	Variable
25	ExprTuple	26
26	Variable