Expression of type Lambda ¶

from the theory of proveit.numbers.division ¶

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, Forall, InSet
from proveit.numbers import Complex, ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Lambda([a, d], Conditional(Forall(instance_param_or_params = [b, c, e], instance_expr = Equals(Mult(frac(Mult(a, b), c), frac(d, Mult(b, e))), Mult(frac(a, c), frac(d, e))), domain = ComplexNonZero), And(InSet(a, Complex), InSet(d, Complex))))

# 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(a, d\right) \mapsto \left\{\forall_{b, c, e \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{a \cdot b}{c} \cdot \frac{d}{b \cdot e}\right) = \left(\frac{a}{c} \cdot \frac{d}{e}\right)\right) \textrm{ if } a \in \mathbb{C} ,  d \in \mathbb{C}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	50, 46
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 31 operands: 13
10	Operation	operator: 31 operands: 14
11	ExprTuple	51, 45, 52
12	Conditional	value: 15 condition: 16
13	ExprTuple	50, 17
14	ExprTuple	46, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 48 operands: 27
23	Operation	operator: 48 operands: 28
24	Operation	operator: 31 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	33, 34
28	ExprTuple	35, 36
29	ExprTuple	51, 37
30	ExprTuple	45, 37
31	Literal
32	ExprTuple	52, 37
33	Operation	operator: 41 operands: 38
34	Operation	operator: 41 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	ExprTuple	43, 45
39	ExprTuple	46, 44
40	ExprTuple	50, 45
41	Literal
42	ExprTuple	46, 52
43	Operation	operator: 48 operands: 47
44	Operation	operator: 48 operands: 49
45	Variable
46	Variable
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	51, 52
50	Variable
51	Variable
52	Variable

Expression of type Lambda¶

from the theory of proveit.numbers.division¶

Expression of type Lambda ¶

from the theory of proveit.numbers.division ¶