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, P, Px, V, W, x
from proveit.linear_algebra import LinMap
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(Px, W), domain = 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\{\forall_{x \in V}~\left(P\left(x\right) \in W\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 operand: 6
2	Operation	operator: 14 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	19, 7
6	Lambda	parameter: 21 body: 8
7	Operation	operator: 9 operands: 10
8	Conditional	value: 11 condition: 12
9	Literal
10	ExprTuple	18, 17
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	21, 18
16	Operation	operator: 19 operand: 21
17	Variable
18	Variable
19	Variable
20	ExprTuple	21
21	Variable