Expression of type ExprTuple

from the theory of proveit.numbers.summation

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, b, l
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Integer, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Add(l, one)
sub_expr2 = InSet(l, Integer)
sub_expr3 = Mult(a, b, sub_expr1)
sub_expr4 = Mult(sub_expr1, Mult(a, b))
expr = ExprTuple(Forall(instance_param_or_params = [l], instance_expr = Equals(sub_expr3, sub_expr4), domain = Integer), Equals(Lambda(l, Conditional(sub_expr3, sub_expr2)), Lambda(l, Conditional(sub_expr4, sub_expr2))).with_wrapping_at(2))

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(\forall_{l \in \mathbb{Z}}~\left(\left(a \cdot b \cdot \left(l + 1\right)\right) = \left(\left(l + 1\right) \cdot \left(a \cdot b\right)\right)\right), \begin{array}{c} \begin{array}{l} \left[l \mapsto \left\{a \cdot b \cdot \left(l + 1\right) \textrm{ if } l \in \mathbb{Z}\right..\right] =  \\ \left[l \mapsto \left\{\left(l + 1\right) \cdot \left(a \cdot b\right) \textrm{ if } l \in \mathbb{Z}\right..\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 30 body: 9
7	Lambda	parameter: 30 body: 10
8	Lambda	parameter: 30 body: 12
9	Conditional	value: 13 condition: 14
10	Conditional	value: 19 condition: 14
11	ExprTuple	30
12	Conditional	value: 20 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	30, 21
19	Operation	operator: 28 operands: 22
20	Operation	operator: 28 operands: 23
21	Literal
22	ExprTuple	32, 33, 24
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Literal
32	Variable
33	Variable