Expression of type Conditional

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, Lambda, P, Px, V, W, c, x
from proveit.linear_algebra import LinMap, ScalarMult
from proveit.logic import Equals, InSet

# build up the expression from sub-expressions
expr = Conditional(Equals(ScalarMult(c, P), Lambda(x, Conditional(ScalarMult(c, Px), InSet(x, V)))), InSet(P, LinMap(V, W)))

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(c \cdot P\right) = \left[x \mapsto \left\{c \cdot P\left(x\right) \textrm{ if } x \in V\right..\right] \textrm{ if } P \in \mathcal{L}\left(V, W\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	23, 8
6	Operation	operator: 16 operands: 9
7	Lambda	parameter: 25 body: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	20, 23
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	22, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	25, 22
20	Variable
21	Operation	operator: 23 operand: 25
22	Variable
23	Variable
24	ExprTuple	25
25	Variable