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 Lambda, alpha, x, y
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Lambda(alpha, Forall(instance_param_or_params = [x, y], instance_expr = Equals(ScalarMult(alpha, x), ScalarMult(alpha, y)), condition = Equals(x, y)))

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())

\alpha \mapsto \left[\forall_{x, y~|~x = y}~\left(\left(\alpha \cdot x\right) = \left(\alpha \cdot y\right)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 18 body: 2
1	ExprTuple	18
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 11 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	17, 19
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Variable