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, VecSpaces
from proveit.logic import Equals, Forall, InClass

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

V \mapsto \left\{\forall_{x \in V}~\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)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\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: 20 body: 2
1	ExprTuple	20
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	20, 9
8	Lambda	parameter: 43 body: 11
9	Operation	operator: 12 operand: 39
10	ExprTuple	43
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	39
14	Operation	operator: 16 operand: 19
15	Operation	operator: 35 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	43, 20
19	Lambda	parameters: 42 body: 21
20	Variable
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 41 operands: 32
29	Operation	operator: 41 operands: 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	ExprTuple	44, 37
33	ExprTuple	38, 43
34	ExprTuple	44, 39
35	Literal
36	ExprTuple	45, 39
37	Operation	operator: 41 operands: 40
38	Operation	operator: 41 operands: 42
39	Variable
40	ExprTuple	45, 43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Variable