Theoria.Library.Bool.Theorems (theoria v0.4.0)

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Theorem corpus for Theoria.Library.Bool.

These proofs document the initial boolean declarations and computation rules accepted by definitional equality.

Summary

Functions

Returns the unelaborated proof syntax for theorem bool_and_false_false.

Elaborates and checks theorem bool_and_false_false against the given environment.

Returns the unelaborated type syntax for theorem bool_and_false_false.

Returns the unelaborated proof syntax for theorem bool_and_false_true.

Elaborates and checks theorem bool_and_false_true against the given environment.

Returns the unelaborated type syntax for theorem bool_and_false_true.

Returns the unelaborated proof syntax for theorem bool_and_true_false.

Elaborates and checks theorem bool_and_true_false against the given environment.

Returns the unelaborated type syntax for theorem bool_and_true_false.

Returns the unelaborated proof syntax for theorem bool_and_true_left.

Elaborates and checks theorem bool_and_true_left against the given environment.

Returns the unelaborated type syntax for theorem bool_and_true_left.

Returns the unelaborated proof syntax for theorem bool_and_true_true.

Elaborates and checks theorem bool_and_true_true against the given environment.

Returns the unelaborated type syntax for theorem bool_and_true_true.

Returns the unelaborated proof syntax for theorem bool_not_false.

Elaborates and checks theorem bool_not_false against the given environment.

Returns the unelaborated type syntax for theorem bool_not_false.

Returns the unelaborated proof syntax for theorem bool_not_is_function.

Elaborates and checks theorem bool_not_is_function against the given environment.

Returns the unelaborated type syntax for theorem bool_not_is_function.

Returns the unelaborated proof syntax for theorem bool_not_true.

Elaborates and checks theorem bool_not_true against the given environment.

Returns the unelaborated type syntax for theorem bool_not_true.

Returns the unelaborated proof syntax for theorem bool_or_false_false.

Elaborates and checks theorem bool_or_false_false against the given environment.

Returns the unelaborated type syntax for theorem bool_or_false_false.

Returns the unelaborated proof syntax for theorem bool_or_false_left.

Elaborates and checks theorem bool_or_false_left against the given environment.

Returns the unelaborated type syntax for theorem bool_or_false_left.

Returns the unelaborated proof syntax for theorem bool_or_false_true.

Elaborates and checks theorem bool_or_false_true against the given environment.

Returns the unelaborated type syntax for theorem bool_or_false_true.

Returns the unelaborated proof syntax for theorem bool_or_true_false.

Elaborates and checks theorem bool_or_true_false against the given environment.

Returns the unelaborated type syntax for theorem bool_or_true_false.

Returns the unelaborated proof syntax for theorem bool_or_true_true.

Elaborates and checks theorem bool_or_true_true against the given environment.

Returns the unelaborated type syntax for theorem bool_or_true_true.

Returns the unelaborated proof syntax for theorem false_is_bool.

Elaborates and checks theorem false_is_bool against the given environment.

Returns the unelaborated type syntax for theorem false_is_bool.

Returns the unelaborated proof syntax for theorem true_is_bool.

Elaborates and checks theorem true_is_bool against the given environment.

Returns the unelaborated type syntax for theorem true_is_bool.

Functions

bool_and_false_false_proof()

Returns the unelaborated proof syntax for theorem bool_and_false_false.

bool_and_false_false_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_and_false_false against the given environment.

bool_and_false_false_type()

Returns the unelaborated type syntax for theorem bool_and_false_false.

bool_and_false_true_proof()

Returns the unelaborated proof syntax for theorem bool_and_false_true.

bool_and_false_true_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_and_false_true against the given environment.

bool_and_false_true_type()

Returns the unelaborated type syntax for theorem bool_and_false_true.

bool_and_true_false_proof()

Returns the unelaborated proof syntax for theorem bool_and_true_false.

bool_and_true_false_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_and_true_false against the given environment.

bool_and_true_false_type()

Returns the unelaborated type syntax for theorem bool_and_true_false.

bool_and_true_left_proof()

Returns the unelaborated proof syntax for theorem bool_and_true_left.

bool_and_true_left_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_and_true_left against the given environment.

bool_and_true_left_type()

Returns the unelaborated type syntax for theorem bool_and_true_left.

bool_and_true_true_proof()

Returns the unelaborated proof syntax for theorem bool_and_true_true.

bool_and_true_true_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_and_true_true against the given environment.

bool_and_true_true_type()

Returns the unelaborated type syntax for theorem bool_and_true_true.

bool_not_false_proof()

Returns the unelaborated proof syntax for theorem bool_not_false.

bool_not_false_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_not_false against the given environment.

bool_not_false_type()

Returns the unelaborated type syntax for theorem bool_not_false.

bool_not_is_function_proof()

Returns the unelaborated proof syntax for theorem bool_not_is_function.

bool_not_is_function_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_not_is_function against the given environment.

bool_not_is_function_type()

Returns the unelaborated type syntax for theorem bool_not_is_function.

bool_not_true_proof()

Returns the unelaborated proof syntax for theorem bool_not_true.

bool_not_true_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_not_true against the given environment.

bool_not_true_type()

Returns the unelaborated type syntax for theorem bool_not_true.

bool_or_false_false_proof()

Returns the unelaborated proof syntax for theorem bool_or_false_false.

bool_or_false_false_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_or_false_false against the given environment.

bool_or_false_false_type()

Returns the unelaborated type syntax for theorem bool_or_false_false.

bool_or_false_left_proof()

Returns the unelaborated proof syntax for theorem bool_or_false_left.

bool_or_false_left_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_or_false_left against the given environment.

bool_or_false_left_type()

Returns the unelaborated type syntax for theorem bool_or_false_left.

bool_or_false_true_proof()

Returns the unelaborated proof syntax for theorem bool_or_false_true.

bool_or_false_true_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_or_false_true against the given environment.

bool_or_false_true_type()

Returns the unelaborated type syntax for theorem bool_or_false_true.

bool_or_true_false_proof()

Returns the unelaborated proof syntax for theorem bool_or_true_false.

bool_or_true_false_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_or_true_false against the given environment.

bool_or_true_false_type()

Returns the unelaborated type syntax for theorem bool_or_true_false.

bool_or_true_true_proof()

Returns the unelaborated proof syntax for theorem bool_or_true_true.

bool_or_true_true_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem bool_or_true_true against the given environment.

bool_or_true_true_type()

Returns the unelaborated type syntax for theorem bool_or_true_true.

false_is_bool_proof()

Returns the unelaborated proof syntax for theorem false_is_bool.

false_is_bool_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem false_is_bool against the given environment.

false_is_bool_type()

Returns the unelaborated type syntax for theorem false_is_bool.

true_is_bool_proof()

Returns the unelaborated proof syntax for theorem true_is_bool.

true_is_bool_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem true_is_bool against the given environment.

true_is_bool_type()

Returns the unelaborated type syntax for theorem true_is_bool.