Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 36 body: 2
1	ExprTuple	36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	36, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	43, 42, 44
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 40 operands: 27
23	Operation	operator: 37 operands: 28
24	Operation	operator: 31 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	43, 33
28	ExprTuple	34, 35
29	ExprTuple	43, 36
30	ExprTuple	42, 36
31	Literal
32	ExprTuple	44, 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	Variable
37	Literal
38	ExprTuple	42, 44
39	ExprTuple	43, 42
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable