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 Conditional, ExprRange, ExprTuple, 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 LessEq, Mult, RealNonNeg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j], Conditional(LessEq(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonNeg), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), RealNonNeg), 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(\left(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \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) \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(b_{1} \in \mathbb{R}^{\ge 0}\right) ,  \left(b_{2} \in \mathbb{R}^{\ge 0}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{R}^{\ge 0}\right) ,  x \leq y\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: 2 body: 3
2	ExprTuple	21, 22
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprRange	lambda_map: 17 start_index: 30 end_index: 28
12	ExprRange	lambda_map: 18 start_index: 30 end_index: 31
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 25, 22
15	Literal
16	ExprTuple	21, 26, 22
17	Lambda	parameter: 41 body: 23
18	Lambda	parameter: 41 body: 24
19	Literal
20	ExprTuple	25, 26
21	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
22	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
23	Operation	operator: 33 operands: 32
24	Operation	operator: 33 operands: 34
25	Variable
26	Variable
27	Lambda	parameter: 41 body: 35
28	Variable
29	Lambda	parameter: 41 body: 36
30	Literal
31	Variable
32	ExprTuple	35, 37
33	Literal
34	ExprTuple	36, 37
35	IndexedVar	variable: 38 index: 41
36	IndexedVar	variable: 39 index: 41
37	Literal
38	Variable
39	Variable
40	ExprTuple	41
41	Variable