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 Equals, Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = 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), domain = VecSpaces(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(K \mapsto \left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\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: 28 body: 2
2	Operation	operator: 22 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 42 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 22 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 50 body: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	50
15	Conditional	value: 19 condition: 20
16	ExprTuple	52, 21
17	Literal
18	ExprTuple	45, 21
19	Operation	operator: 22 operand: 27
20	Operation	operator: 48 operands: 24
21	Operation	operator: 25 operand: 28
22	Literal
23	ExprTuple	27
24	ExprTuple	50, 28
25	Literal
26	ExprTuple	28
27	Lambda	parameter: 53 body: 30
28	Variable
29	ExprTuple	53
30	Conditional	value: 31 condition: 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 48 operands: 35
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	53, 38
36	Operation	operator: 46 operands: 39
37	Lambda	parameter: 55 body: 40
38	Operation	operator: 41 operands: 42
39	ExprTuple	50, 53
40	Conditional	value: 43 condition: 44
41	Literal
42	ExprTuple	52, 45
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operands: 49
45	Variable
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	55, 52
50	Variable
51	Operation	operator: 53 operand: 55
52	Variable
53	Variable
54	ExprTuple	55
55	Variable