Expression of type ExprTuple

from the theory of proveit.numbers.division

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, a, x, y
from proveit.logic import Forall, InSet
from proveit.numbers import LessEq, RealNeg, RealNonPos, frac

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(Forall(instance_param_or_params = [x, y], instance_expr = LessEq(frac(a, x), frac(a, y)), domain = RealNeg, condition = LessEq(x, y)), InSet(a, RealNonPos))))

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 \mapsto \left\{\forall_{x, y \in \mathbb{R}^-~|~x \leq y}~\left(\frac{a}{x} \leq \frac{a}{y}\right) \textrm{ if } a \in \mathbb{R}^{\le 0}\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	parameter: 30 body: 3
2	ExprTuple	30
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 26 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	30, 10
9	Lambda	parameters: 29 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 28 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operands: 29
22	ExprTuple	30, 32
23	Literal
24	ExprTuple	30, 33
25	ExprTuple	32, 31
26	Literal
27	ExprTuple	33, 31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Literal
32	Variable
33	Variable