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, x, y, z
from proveit.linear_algebra import InnerProd, InnerProdSpaces, VecAdd
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 = [x, y, z], instance_expr = Equals(InnerProd(x, VecAdd(y, z)), VecAdd(InnerProd(x, y), InnerProd(x, z))), domain = H), 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_{x, y, z \in H}~\left(\left \langle x, y + z\right \rangle = \left(\left \langle x, y\right \rangle + \left \langle x, z\right \rangle\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: 21 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 40 body: 6
5	ExprTuple	40
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	40, 14
13	Lambda	parameters: 15 body: 16
14	Operation	operator: 17 operand: 21
15	ExprTuple	47, 46, 48
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29, 30
26	Operation	operator: 44 operands: 31
27	Operation	operator: 41 operands: 32
28	Operation	operator: 35 operands: 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	ExprTuple	47, 37
32	ExprTuple	38, 39
33	ExprTuple	47, 40
34	ExprTuple	46, 40
35	Literal
36	ExprTuple	48, 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 44 operands: 43
39	Operation	operator: 44 operands: 45
40	Variable
41	Literal
42	ExprTuple	46, 48
43	ExprTuple	47, 46
44	Literal
45	ExprTuple	47, 48
46	Variable
47	Variable
48	Variable