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, Lambda, v, w
from proveit.linear_algebra import InnerProd, InnerProdSpaces, Norm
from proveit.logic import Forall, InClass
from proveit.numbers import Complex, Exp, LessEq, Mult, two

# build up the expression from sub-expressions
expr = Lambda(H, Conditional(Forall(instance_param_or_params = [v, w], instance_expr = LessEq(Exp(Norm(InnerProd(v, w)), two), Mult(InnerProd(v, v), InnerProd(w, w))), domain = H), InClass(H, InnerProdSpaces(Complex))))

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_{v, w \in H}~\left(\left \|\left \langle v, w\right \rangle\right \|^{2} \leq \left(\left \langle v, v\right \rangle \cdot \left \langle w, w\right \rangle\right)\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(\mathbb{C}\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: 43 body: 11
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32, 33
27	Literal
28	ExprTuple	34, 35
29	ExprTuple	44, 36
30	Literal
31	ExprTuple	45, 36
32	Operation	operator: 37 operand: 41
33	Literal
34	Operation	operator: 42 operands: 39
35	Operation	operator: 42 operands: 40
36	Variable
37	Literal
38	ExprTuple	41
39	ExprTuple	44, 44
40	ExprTuple	45, 45
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Variable