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, ExprTuple, Lambda, i, j, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Less, Mult, Natural, RealPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [x, y], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Less(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j)), domain = RealPos, condition = Less(x, y))), And(InSet(i, Natural), InSet(j, Natural)))))

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(i, j\right) \mapsto \left\{\forall_{x, y}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{R}^+~|~x < 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) < \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] \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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	44, 47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 23 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 36 body: 11
9	Operation	operator: 49 operands: 12
10	Operation	operator: 49 operands: 13
11	Operation	operator: 14 operand: 17
12	ExprTuple	44, 16
13	ExprTuple	47, 16
14	Literal
15	ExprTuple	17
16	Literal
17	Lambda	parameters: 18 body: 19
18	ExprTuple	37, 38
19	Conditional	value: 20 condition: 21
20	Operation	operator: 35 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprRange	lambda_map: 33 start_index: 46 end_index: 44
28	ExprRange	lambda_map: 34 start_index: 46 end_index: 47
29	Operation	operator: 35 operands: 36
30	ExprTuple	37, 41, 38
31	Literal
32	ExprTuple	37, 42, 38
33	Lambda	parameter: 57 body: 39
34	Lambda	parameter: 57 body: 40
35	Literal
36	ExprTuple	41, 42
37	ExprRange	lambda_map: 43 start_index: 46 end_index: 44
38	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
39	Operation	operator: 49 operands: 48
40	Operation	operator: 49 operands: 50
41	Variable
42	Variable
43	Lambda	parameter: 57 body: 51
44	Variable
45	Lambda	parameter: 57 body: 52
46	Literal
47	Variable
48	ExprTuple	51, 53
49	Literal
50	ExprTuple	52, 53
51	IndexedVar	variable: 54 index: 57
52	IndexedVar	variable: 55 index: 57
53	Literal
54	Variable
55	Variable
56	ExprTuple	57
57	Variable