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, ExprRange, IndexedVar, Lambda, Variable, a, b, c, 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, Real, RealNonNeg, greater_eq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, c_1_to_j], Conditional(Forall(instance_param_or_params = [b], instance_expr = greater_eq(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonNeg), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), RealNonNeg), one, j))))

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(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{j}\right) \mapsto \left\{\forall_{b \in \mathbb{R}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \geq b\right) \textrm{ if } \left(a_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(a_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{R}^{\ge 0}\right), \left(c_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(c_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{R}^{\ge 0}\right)\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	31, 33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 32 body: 13
10	ExprRange	lambda_map: 14 start_index: 37 end_index: 35
11	ExprRange	lambda_map: 15 start_index: 37 end_index: 38
12	ExprTuple	32
13	Conditional	value: 16 condition: 17
14	Lambda	parameter: 44 body: 18
15	Lambda	parameter: 44 body: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 24 operands: 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	32, 26
22	ExprTuple	32, 27
23	ExprTuple	39, 28
24	Literal
25	ExprTuple	40, 28
26	Operation	operator: 29 operands: 30
27	Literal
28	Literal
29	Literal
30	ExprTuple	31, 32, 33
31	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
32	Variable
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	Lambda	parameter: 44 body: 39
35	Variable
36	Lambda	parameter: 44 body: 40
37	Literal
38	Variable
39	IndexedVar	variable: 41 index: 44
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable