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 A, B, Conditional, ExprTuple, Function, K, Lambda, V, W, x
from proveit.linear_algebra import LinMap, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = Forall(instance_param_or_params = [A, B], instance_expr = Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), domain = LinMap(V, W)), 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_{A, B \in \mathcal{L}\left(V, W\right)}~\left(\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\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: 31 body: 2
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 44 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 23 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameters: 32 body: 14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	Conditional	value: 18 condition: 19
15	ExprTuple	47, 20
16	Literal
17	ExprTuple	48, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operand: 31
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	31
27	Operation	operator: 39 operands: 32
28	Lambda	parameter: 52 body: 33
29	Operation	operator: 41 operands: 34
30	Operation	operator: 41 operands: 35
31	Variable
32	ExprTuple	49, 50
33	Conditional	value: 36 condition: 37
34	ExprTuple	49, 38
35	ExprTuple	50, 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	ExprTuple	45, 46
41	Literal
42	ExprTuple	52, 47
43	Literal
44	ExprTuple	47, 48
45	Operation	operator: 49 operand: 52
46	Operation	operator: 50 operand: 52
47	Variable
48	Variable
49	Variable
50	Variable
51	ExprTuple	52
52	Variable