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, a, b, x, y
from proveit.linear_algebra import VecSpaces, binary_lin_comb_ax_by
from proveit.logic import Forall, InClass, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = InSet(binary_lin_comb_ax_by, V), domain = V), domain = K), InClass(V, VecSpaces(K)))

# 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_{a, b \in K}~\left[\forall_{x, y \in V}~\left(\left(\left(a \cdot x\right) + \left(b \cdot y\right)\right) \in V\right)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 14 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	40, 7
6	Lambda	parameters: 8 body: 9
7	Operation	operator: 10 operand: 26
8	ExprTuple	44, 46
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	26
12	Operation	operator: 14 operand: 17
13	Operation	operator: 28 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	18, 19
17	Lambda	parameters: 20 body: 21
18	Operation	operator: 36 operands: 22
19	Operation	operator: 36 operands: 23
20	ExprTuple	45, 47
21	Conditional	value: 24 condition: 25
22	ExprTuple	44, 26
23	ExprTuple	46, 26
24	Operation	operator: 36 operands: 27
25	Operation	operator: 28 operands: 29
26	Variable
27	ExprTuple	30, 40
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	45, 40
36	Literal
37	ExprTuple	47, 40
38	Operation	operator: 42 operands: 41
39	Operation	operator: 42 operands: 43
40	Variable
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46, 47
44	Variable
45	Variable
46	Variable
47	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.scalar_multiplication¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.scalar_multiplication ¶