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, 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 = ExprTuple(Lambda(P, 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(P \mapsto \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..\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: 26 body: 3
2	ExprTuple	26
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	26, 11
9	Operation	operator: 19 operands: 12
10	Lambda	parameter: 28 body: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	23, 26
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	25, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	28, 25
23	Variable
24	Operation	operator: 26 operand: 28
25	Variable
26	Variable
27	ExprTuple	28
28	Variable