Expression of type Conditional ¶

from the theory of proveit.linear_algebra ¶

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, Function, S, T, V, W, v
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
sub_expr2 = LinMap(V, W)
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), domain = V), And(InSet(S, sub_expr2), InSet(T, sub_expr2)))

# 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}~\left(\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right)\right) \textrm{ if } S \in \mathcal{L}\left(V, W\right) ,  T \in \mathcal{L}\left(V, W\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 36 body: 10
8	Operation	operator: 18 operands: 11
9	Operation	operator: 18 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	33, 15
12	ExprTuple	34, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	36, 24
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operand: 36
23	Operation	operator: 27 operands: 28
24	Variable
25	Variable
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 33 operand: 36
32	Operation	operator: 34 operand: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra ¶