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, a, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Forall, InSet

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

a \mapsto \left\{\forall_{x \in V}~\left(\left(a \cdot x\right) \in V\right) \textrm{ if } a \in K\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 21 body: 2
1	ExprTuple	21
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 15 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	21, 9
8	Lambda	parameter: 22 body: 11
9	Variable
10	ExprTuple	22
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	22, 18
17	Operation	operator: 19 operands: 20
18	Variable
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Variable