Expression of type ExprTuple

from the theory of proveit.linear_algebra.linear_maps

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, Function, K, Lambda, P, Px, V, c, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(c, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Function(P, [ScalarMult(c, x)]), ScalarMult(c, Px)), domain = V), InSet(c, 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(c \mapsto \left\{\forall_{x \in V}~\left(P\left(c \cdot x\right) = \left(c \cdot P\left(x\right)\right)\right) \textrm{ if } c \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	parameter: 29 body: 3
2	ExprTuple	29
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 16 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	29, 10
9	Lambda	parameter: 30 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	30, 20
18	Operation	operator: 27 operand: 23
19	Operation	operator: 25 operands: 22
20	Variable
21	ExprTuple	23
22	ExprTuple	29, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operand: 30
25	Literal
26	ExprTuple	29, 30
27	Variable
28	ExprTuple	30
29	Variable
30	Variable