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 Lambda, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import Forall
from proveit.numbers import Add, LessEq, Real

# build up the expression from sub-expressions
expr = Lambda([x, y], Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = LessEq(Add(a_1_to_i, x, b_1_to_j), Add(a_1_to_i, y, b_1_to_j)), domain = Real, condition = 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(x, y\right) \mapsto \left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{R}~|~x \leq y}~\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)\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: 23 body: 1
1	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	24, 25
6	Conditional	value: 7 condition: 8
7	Operation	operator: 22 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprRange	lambda_map: 20 start_index: 33 end_index: 31
15	ExprRange	lambda_map: 21 start_index: 33 end_index: 34
16	Operation	operator: 22 operands: 23
17	ExprTuple	24, 28, 25
18	Literal
19	ExprTuple	24, 29, 25
20	Lambda	parameter: 44 body: 26
21	Lambda	parameter: 44 body: 27
22	Literal
23	ExprTuple	28, 29
24	ExprRange	lambda_map: 30 start_index: 33 end_index: 31
25	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
26	Operation	operator: 36 operands: 35
27	Operation	operator: 36 operands: 37
28	Variable
29	Variable
30	Lambda	parameter: 44 body: 38
31	Variable
32	Lambda	parameter: 44 body: 39
33	Literal
34	Variable
35	ExprTuple	38, 40
36	Literal
37	ExprTuple	39, 40
38	IndexedVar	variable: 41 index: 44
39	IndexedVar	variable: 42 index: 44
40	Literal
41	Variable
42	Variable
43	ExprTuple	44
44	Variable