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 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 20 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 39 body: 5
4	ExprTuple	39
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	39, 13
12	Lambda	parameters: 14 body: 15
13	Operation	operator: 16 operand: 20
14	ExprTuple	46, 45, 47
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	Operation	operator: 43 operands: 30
26	Operation	operator: 40 operands: 31
27	Operation	operator: 34 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	46, 36
31	ExprTuple	37, 38
32	ExprTuple	46, 39
33	ExprTuple	45, 39
34	Literal
35	ExprTuple	47, 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 43 operands: 42
38	Operation	operator: 43 operands: 44
39	Variable
40	Literal
41	ExprTuple	45, 47
42	ExprTuple	46, 45
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Variable