logo

Expression of type Implies

from the theory of proveit.linear_algebra.tensors

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, beta, gamma, i
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Add, Interval, Mult, four, one, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(gamma, beta)
sub_expr2 = Add(i, one)
sub_expr3 = Interval(two, four)
sub_expr4 = Mult(sub_expr1, i, sub_expr2)
sub_expr5 = InSet(i, sub_expr3)
sub_expr6 = Mult(sub_expr1, Mult(i, sub_expr2))
expr = Implies(Forall(instance_param_or_params = [i], instance_expr = Equals(sub_expr4, sub_expr6), domain = sub_expr3), Equals(Lambda(i, Conditional(sub_expr4, sub_expr5)), Lambda(i, Conditional(sub_expr6, sub_expr5))).with_wrapping_at(2)).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left[\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(\left(\gamma \cdot \beta\right) \cdot i \cdot \left(i + 1\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(i \cdot \left(i + 1\right)\right)\right)\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot i \cdot \left(i + 1\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot \left(i \cdot \left(i + 1\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] \end{array} \end{array}\right) \end{array} \end{array}
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.()(2)('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: 5
operand: 8
4Operationoperator: 17
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameter: 40
body: 11
9Lambdaparameter: 40
body: 12
10Lambdaparameter: 40
body: 14
11Conditionalvalue: 15
condition: 16
12Conditionalvalue: 21
condition: 16
13ExprTuple40
14Conditionalvalue: 22
condition: 16
15Operationoperator: 17
operands: 18
16Operationoperator: 19
operands: 20
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple40, 23
21Operationoperator: 33
operands: 24
22Operationoperator: 33
operands: 25
23Operationoperator: 26
operands: 27
24ExprTuple28, 40, 37
25ExprTuple28, 29
26Literal
27ExprTuple30, 31
28Operationoperator: 33
operands: 32
29Operationoperator: 33
operands: 34
30Literal
31Literal
32ExprTuple35, 36
33Literal
34ExprTuple40, 37
35Variable
36Variable
37Operationoperator: 38
operands: 39
38Literal
39ExprTuple40, 41
40Variable
41Literal