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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, fi, gamma, i
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Interval, Mult, four, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = InSet(i, Interval(two, four))
sub_expr2 = Conditional(ScalarMult(ScalarMult(gamma, beta), fi), sub_expr1)
sub_expr3 = Conditional(ScalarMult(Mult(gamma, beta), fi), sub_expr1)
expr = Implies(Forall(instance_param_or_params = [i], instance_expr = Equals(sub_expr2, sub_expr3)), Equals(Lambda(i, sub_expr2), Lambda(i, sub_expr3)).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}~\left(\left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.. = \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\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: 12
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameter: 36
body: 11
9Lambdaparameter: 36
body: 14
10Lambdaparameter: 36
body: 15
11Operationoperator: 12
operands: 13
12Literal
13ExprTuple14, 15
14Conditionalvalue: 16
condition: 18
15Conditionalvalue: 17
condition: 18
16Operationoperator: 27
operands: 19
17Operationoperator: 27
operands: 20
18Operationoperator: 21
operands: 22
19ExprTuple23, 25
20ExprTuple24, 25
21Literal
22ExprTuple36, 26
23Operationoperator: 27
operands: 29
24Operationoperator: 28
operands: 29
25Operationoperator: 30
operand: 36
26Operationoperator: 32
operands: 33
27Literal
28Literal
29ExprTuple34, 35
30Variable
31ExprTuple36
32Literal
33ExprTuple37, 38
34Variable
35Variable
36Variable
37Literal
38Literal