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

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