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, v
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
expr = Lambda(K, Conditional(Forall(instance_param_or_params = [v, V], instance_expr = Equals(ScalarMult(one, v), v), domains = [V, VecSpaces(K)]), InSet(one, 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_{v \in V, V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\left(1 \cdot v\right) = v\right) \textrm{ if } 1 \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: 30 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 20 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	24, 30
7	Lambda	parameters: 21 body: 8
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 25
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	26, 27
24	Literal
25	Variable
26	Variable
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Variable