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, x, y, z
from proveit.linear_algebra import InnerProd, InnerProdSpaces, VecAdd
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(H, Conditional(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), 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_{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) \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: 37 body: 3
2	ExprTuple	37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	37, 11
10	Lambda	parameters: 12 body: 13
11	Operation	operator: 14 operand: 18
12	ExprTuple	44, 43, 45
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 41 operands: 28
24	Operation	operator: 38 operands: 29
25	Operation	operator: 32 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	44, 34
29	ExprTuple	35, 36
30	ExprTuple	44, 37
31	ExprTuple	43, 37
32	Literal
33	ExprTuple	45, 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Variable
38	Literal
39	ExprTuple	43, 45
40	ExprTuple	44, 43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Variable