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Theorem euclids_lemma of type Forall

from the theory of proveit.numbers.divisibility

see dependencies

In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.divisibility import euclids_lemma
In [2]:
# check that the built expression is the same as the stored expression
assert euclids_lemma.expr == stored_expr
assert euclids_lemma.expr._style_id == stored_expr._style_id
print("Passed sanity check: euclids_lemma matches stored_expr")
Passed sanity check: euclids_lemma matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{x, y, z \in \mathbb{Z}~|~x \rvert \left(y \cdot z\right), gcd\left(x, y\right) = 1}~\left(x \rvert z\right)
In [4]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple33, 34, 32
5Conditionalvalue: 6
condition: 7
6Operationoperator: 20
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple33, 32
9Literal
10ExprTuple11, 12, 13, 14, 15
11Operationoperator: 18
operands: 16
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14Operationoperator: 20
operands: 21
15Operationoperator: 22
operands: 23
16ExprTuple33, 24
17ExprTuple34, 24
18Literal
19ExprTuple32, 24
20Literal
21ExprTuple33, 25
22Literal
23ExprTuple26, 27
24Literal
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27Literal
28Literal
29ExprTuple34, 32
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Variable