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

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P], instance_expr = Equals(ScalarMult(c, P), Lambda(x, Conditional(ScalarMult(c, Px), InSet(x, V)))), domain = LinMap(V, W)), 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\{\forall_{P \in \mathcal{L}\left(V, W\right)}~\left(\left(c \cdot P\right) = \left[x \mapsto \left\{c \cdot P\left(x\right) \textrm{ if } x \in V\right..\right]\right) \textrm{ if } c \in K\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: 27 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	29, 7
6	Lambda	parameter: 32 body: 9
7	Variable
8	ExprTuple	32
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 27 operands: 14
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	32, 17
15	Operation	operator: 25 operands: 18
16	Lambda	parameter: 34 body: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	29, 32
19	Conditional	value: 22 condition: 23
20	Literal
21	ExprTuple	31, 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Variable
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	34, 31
29	Variable
30	Operation	operator: 32 operand: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable