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Expression of type Lambda

from the theory of proveit.numbers.division

In [1]:
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, a, b, c, d, e
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Mult, frac
In [2]:
# build up the expression from sub-expressions
expr = Lambda([b, c, e], Conditional(Equals(Mult(frac(Mult(a, b), c), frac(d, Mult(b, e))), Mult(frac(a, c), frac(d, e))), And(InSet(b, ComplexNonZero), InSet(c, ComplexNonZero), InSet(e, ComplexNonZero))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(b, c, e\right) \mapsto \left\{\left(\frac{a \cdot b}{c} \cdot \frac{d}{b \cdot e}\right) = \left(\frac{a}{c} \cdot \frac{d}{e}\right) \textrm{ if } b \in \mathbb{C}^{\neq 0} ,  c \in \mathbb{C}^{\neq 0} ,  e \in \mathbb{C}^{\neq 0}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple38, 32, 39
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 35
operands: 14
10Operationoperator: 35
operands: 15
11Operationoperator: 18
operands: 16
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14ExprTuple20, 21
15ExprTuple22, 23
16ExprTuple38, 24
17ExprTuple32, 24
18Literal
19ExprTuple39, 24
20Operationoperator: 28
operands: 25
21Operationoperator: 28
operands: 26
22Operationoperator: 28
operands: 27
23Operationoperator: 28
operands: 29
24Literal
25ExprTuple30, 32
26ExprTuple33, 31
27ExprTuple37, 32
28Literal
29ExprTuple33, 39
30Operationoperator: 35
operands: 34
31Operationoperator: 35
operands: 36
32Variable
33Variable
34ExprTuple37, 38
35Literal
36ExprTuple38, 39
37Variable
38Variable
39Variable