Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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, beta, fi, gamma, i
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Interval, Mult, four, two

# build up the expression from sub-expressions
sub_expr1 = InSet(i, Interval(two, four))
expr = Forall(instance_param_or_params = [i], instance_expr = Equals(Conditional(ScalarMult(ScalarMult(gamma, beta), fi), sub_expr1), Conditional(ScalarMult(Mult(gamma, beta), fi), sub_expr1)))

expr:

# 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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 29 body: 4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Conditional	value: 9 condition: 11
8	Conditional	value: 10 condition: 11
9	Operation	operator: 20 operands: 12
10	Operation	operator: 20 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	16, 18
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	29, 19
16	Operation	operator: 20 operands: 22
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 29
19	Operation	operator: 25 operands: 26
20	Literal
21	Literal
22	ExprTuple	27, 28
23	Variable
24	ExprTuple	29
25	Literal
26	ExprTuple	30, 31
27	Variable
28	Variable
29	Variable
30	Literal
31	Literal