Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_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, K, Lambda, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([alpha, beta], Conditional(Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), And(InSet(alpha, K), InSet(beta, K)))))

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(\alpha, \beta\right) \mapsto \left\{\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right) \textrm{ if } \alpha \in K ,  \beta \in K\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: 23 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 22 operands: 13
10	Operation	operator: 22 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	25, 18
14	ExprTuple	19, 24
15	ExprTuple	25, 20
16	Literal
17	ExprTuple	26, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	26, 24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable