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, V, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet

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

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(x \mapsto \left\{\forall_{\alpha, \beta \in K}~\left(\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right)\right) \textrm{ if } x \in V\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: 33 body: 3
2	ExprTuple	33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 25 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	33, 10
9	Lambda	parameters: 32 body: 11
10	Variable
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 31 operands: 22
19	Operation	operator: 31 operands: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	34, 27
23	ExprTuple	28, 33
24	ExprTuple	34, 29
25	Literal
26	ExprTuple	35, 29
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operands: 32
29	Variable
30	ExprTuple	35, 33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Variable