Expression of type Implies

from the theory of proveit.logic.booleans.conjunction

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 C, IndexedVar, Variable, n
from proveit.core_expr_types import C_1_to_n
from proveit.logic import And, Forall, Implies
from proveit.numbers import Interval, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Implies(And(C_1_to_n), Forall(instance_param_or_params = [sub_expr1], instance_expr = IndexedVar(C, sub_expr1), domain = Interval(one, n)))

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())

\left(C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \Rightarrow \left[\forall_{{_{-}a} \in \{1~\ldotp \ldotp~n\}}~C_{{_{-}a}}\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(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')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	ExprRange	lambda_map: 11 start_index: 23 end_index: 24
10	Lambda	parameter: 19 body: 12
11	Lambda	parameter: 19 body: 13
12	Conditional	value: 13 condition: 14
13	IndexedVar	variable: 15 index: 19
14	Operation	operator: 17 operands: 18
15	Variable
16	ExprTuple	19
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Variable