Expression of type Conditional

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, 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 = 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())

\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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