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 K, Lambda, V, W
from proveit.linear_algebra import LinMap, VecSpaces
from proveit.logic import Forall, InClass

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = InClass(LinMap(V, W), sub_expr1), domain = sub_expr1))

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())

K \mapsto \left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\mathcal{L}\left(V, W\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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