Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, beta, fi, gamma, i
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Interval, Mult, four, two

# build up the expression from sub-expressions
sub_expr1 = InSet(i, Interval(two, four))
sub_expr2 = Conditional(ScalarMult(ScalarMult(gamma, beta), fi), sub_expr1)
sub_expr3 = Conditional(ScalarMult(Mult(gamma, beta), fi), sub_expr1)
expr = ExprTuple(Forall(instance_param_or_params = [i], instance_expr = Equals(sub_expr2, sub_expr3)), Equals(Lambda(i, sub_expr2), Lambda(i, sub_expr3)).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_{i}~\left(\left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.. = \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right), \begin{array}{c} \begin{array}{l} \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\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: 10 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 34 body: 9
7	Lambda	parameter: 34 body: 12
8	Lambda	parameter: 34 body: 13
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Conditional	value: 14 condition: 16
13	Conditional	value: 15 condition: 16
14	Operation	operator: 25 operands: 17
15	Operation	operator: 25 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	21, 23
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	34, 24
21	Operation	operator: 25 operands: 27
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 34
24	Operation	operator: 30 operands: 31
25	Literal
26	Literal
27	ExprTuple	32, 33
28	Variable
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	Variable
33	Variable
34	Variable
35	Literal
36	Literal