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, i, j, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, InSet
from proveit.numbers import Add, LessEq, Real, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j], Conditional(LessEq(Add(a_1_to_i, x, b_1_to_j), Add(a_1_to_i, y, b_1_to_j)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Real), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Real), one, j), LessEq(x, y))))

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