Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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 ExprTuple, 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 LessEq, Mult, RealNonNeg

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = LessEq(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j)), domain = RealNonNeg, 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(\left(x, y\right) \mapsto \left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{R}^{\ge 0}~|~x \leq y}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot x\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) \leq \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot y\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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