Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

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, V, a, b, x, y
from proveit.linear_algebra import VecSpaces, binary_lin_comb_ax_by
from proveit.logic import Forall, InClass, InSet

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