Expression of type Lambda

from the theory of proveit.trigonometry

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, Lambda, t
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, Real
from proveit.trigonometry import Cos

# build up the expression from sub-expressions
expr = Lambda(t, Conditional(Equals(Abs(Cos(t)), Cos(Abs(t))), InSet(t, Real)))

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())

t \mapsto \left\{\left|\cos{t}\right| = \cos{\left|t\right|} \textrm{ if } t \in \mathbb{R}\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: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	18, 10
8	Operation	operator: 16 operand: 13
9	Operation	operator: 15 operand: 14
10	Literal
11	ExprTuple	13
12	ExprTuple	14
13	Operation	operator: 15 operand: 18
14	Operation	operator: 16 operand: 18
15	Literal
16	Literal
17	ExprTuple	18
18	Variable