Expression of type ExprTuple

from the theory of proveit.linear_algebra.linear_maps

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, ExprTuple, K, Lambda, P, Px, V, W, c, x
from proveit.linear_algebra import LinMap, ScalarMult
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(c, Conditional(Forall(instance_param_or_params = [P], instance_expr = Equals(ScalarMult(c, P), Lambda(x, Conditional(ScalarMult(c, Px), InSet(x, V)))), domain = LinMap(V, W)), InSet(c, 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(c \mapsto \left\{\forall_{P \in \mathcal{L}\left(V, W\right)}~\left(\left(c \cdot P\right) = \left[x \mapsto \left\{c \cdot P\left(x\right) \textrm{ if } x \in V\right..\right]\right) \textrm{ if } c \in K\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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