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

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

\left(\left(V, W\right) \mapsto \left\{\forall_{c \in K}~\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)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) ,  W \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	ExprTuple	1
1	Lambda	parameters: 39 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 19 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 47 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	47
12	Conditional	value: 16 condition: 17
13	ExprTuple	49, 18
14	Literal
15	ExprTuple	42, 18
16	Operation	operator: 19 operand: 24
17	Operation	operator: 45 operands: 21
18	Operation	operator: 22 operand: 25
19	Literal
20	ExprTuple	24
21	ExprTuple	47, 25
22	Literal
23	ExprTuple	25
24	Lambda	parameter: 50 body: 27
25	Variable
26	ExprTuple	50
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 45 operands: 32
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	50, 35
33	Operation	operator: 43 operands: 36
34	Lambda	parameter: 52 body: 37
35	Operation	operator: 38 operands: 39
36	ExprTuple	47, 50
37	Conditional	value: 40 condition: 41
38	Literal
39	ExprTuple	49, 42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operands: 46
42	Variable
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	52, 49
47	Variable
48	Operation	operator: 50 operand: 52
49	Variable
50	Variable
51	ExprTuple	52
52	Variable