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, VecSpaces
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [alpha, beta], instance_expr = Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), domain = K), domain = V), InClass(V, VecSpaces(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(V \mapsto \left\{\forall_{x \in V}~\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)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 21 body: 3
2	ExprTuple	21
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	21, 10
9	Lambda	parameter: 44 body: 12
10	Operation	operator: 13 operand: 40
11	ExprTuple	44
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	40
15	Operation	operator: 17 operand: 20
16	Operation	operator: 36 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	44, 21
20	Lambda	parameters: 43 body: 22
21	Variable
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 42 operands: 33
30	Operation	operator: 42 operands: 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	ExprTuple	45, 38
34	ExprTuple	39, 44
35	ExprTuple	45, 40
36	Literal
37	ExprTuple	46, 40
38	Operation	operator: 42 operands: 41
39	Operation	operator: 42 operands: 43
40	Variable
41	ExprTuple	46, 44
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Variable
46	Variable