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Expression of type Equals

from the theory of proveit.numbers.modular

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 L, S, c, x
from proveit.logic import Card, Equals, SetOfAll
from proveit.numbers import Add, Mod
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(Add(c, x), L), domain = S)), Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(x, L), domain = S)))
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\{\left(c + x\right) ~\textup{mod}~ L\right\}_{x \in S}| = |\left\{x ~\textup{mod}~ L\right\}_{x \in S}|
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8Operationoperator: 11
operand: 13
9Operationoperator: 11
operand: 14
10ExprTuple13
11Literal
12ExprTuple14
13Lambdaparameter: 32
body: 15
14Lambdaparameter: 32
body: 17
15Conditionalvalue: 18
condition: 20
16ExprTuple32
17Conditionalvalue: 19
condition: 20
18Operationoperator: 22
operands: 21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21ExprTuple26, 27
22Literal
23ExprTuple32, 27
24Literal
25ExprTuple32, 28
26Operationoperator: 29
operands: 30
27Variable
28Variable
29Literal
30ExprTuple31, 32
31Variable
32Variable