Expression of type Lambda

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 = Lambda(c, 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())

c \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 31 body: 2
1	ExprTuple	31
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	31, 9
8	Lambda	parameter: 34 body: 11
9	Variable
10	ExprTuple	34
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 29 operands: 16
14	Literal
15	ExprTuple	17, 18
16	ExprTuple	34, 19
17	Operation	operator: 27 operands: 20
18	Lambda	parameter: 36 body: 21
19	Operation	operator: 22 operands: 23
20	ExprTuple	31, 34
21	Conditional	value: 24 condition: 25
22	Literal
23	ExprTuple	33, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Variable
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	36, 33
31	Variable
32	Operation	operator: 34 operand: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable