Expression of type ExprTuple

from the theory of proveit.linear_algebra.inner_products

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, H, K, Lambda, a, x, y
from proveit.linear_algebra import InnerProd, InnerProdSpaces, ScalarMult
from proveit.logic import Equals, Forall, InClass

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