Expression of type Lambda

from the theory of proveit.linear_algebra.scalar_multiplication

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, K, Lambda, V, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Forall(instance_param_or_params = [alpha, beta], instance_expr = Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), domain = K), InSet(x, V)))

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())

x \mapsto \left\{\forall_{\alpha, \beta \in K}~\left(\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right)\right) \textrm{ if } x \in V\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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