Theoria.Library.List.Theorems (theoria v0.3.0)

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Theorem corpus for Theoria.Library.List.

These proofs document polymorphic list constructors and the first length computation over the standard Nat-backed list environment.

Summary

Functions

Returns the unelaborated proof syntax for theorem list_append_cons_left.

Elaborates and checks theorem list_append_cons_left against the given environment.

Returns the unelaborated type syntax for theorem list_append_cons_left.

Returns the unelaborated proof syntax for theorem list_append_nil_left.

Elaborates and checks theorem list_append_nil_left against the given environment.

Returns the unelaborated type syntax for theorem list_append_nil_left.

Returns the unelaborated proof syntax for theorem list_cons_is_function.

Elaborates and checks theorem list_cons_is_function against the given environment.

Returns the unelaborated type syntax for theorem list_cons_is_function.

Returns the unelaborated proof syntax for theorem list_length_cons_nil.

Elaborates and checks theorem list_length_cons_nil against the given environment.

Returns the unelaborated type syntax for theorem list_length_cons_nil.

Returns the unelaborated proof syntax for theorem list_length_cons.

Elaborates and checks theorem list_length_cons against the given environment.

Returns the unelaborated type syntax for theorem list_length_cons.

Returns the unelaborated proof syntax for theorem list_length_nil.

Elaborates and checks theorem list_length_nil against the given environment.

Returns the unelaborated type syntax for theorem list_length_nil.

Returns the unelaborated proof syntax for theorem list_length_singleton.

Elaborates and checks theorem list_length_singleton against the given environment.

Returns the unelaborated type syntax for theorem list_length_singleton.

Returns the unelaborated proof syntax for theorem list_length_two.

Elaborates and checks theorem list_length_two against the given environment.

Returns the unelaborated type syntax for theorem list_length_two.

Returns the unelaborated proof syntax for theorem list_nil_is_list.

Elaborates and checks theorem list_nil_is_list against the given environment.

Returns the unelaborated type syntax for theorem list_nil_is_list.

Functions

list_append_cons_left_proof()

Returns the unelaborated proof syntax for theorem list_append_cons_left.

list_append_cons_left_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_append_cons_left against the given environment.

list_append_cons_left_type()

Returns the unelaborated type syntax for theorem list_append_cons_left.

list_append_nil_left_proof()

Returns the unelaborated proof syntax for theorem list_append_nil_left.

list_append_nil_left_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_append_nil_left against the given environment.

list_append_nil_left_type()

Returns the unelaborated type syntax for theorem list_append_nil_left.

list_cons_is_function_proof()

Returns the unelaborated proof syntax for theorem list_cons_is_function.

list_cons_is_function_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_cons_is_function against the given environment.

list_cons_is_function_type()

Returns the unelaborated type syntax for theorem list_cons_is_function.

list_length_cons_nil_proof()

Returns the unelaborated proof syntax for theorem list_length_cons_nil.

list_length_cons_nil_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_length_cons_nil against the given environment.

list_length_cons_nil_type()

Returns the unelaborated type syntax for theorem list_length_cons_nil.

list_length_cons_proof()

Returns the unelaborated proof syntax for theorem list_length_cons.

list_length_cons_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_length_cons against the given environment.

list_length_cons_type()

Returns the unelaborated type syntax for theorem list_length_cons.

list_length_nil_proof()

Returns the unelaborated proof syntax for theorem list_length_nil.

list_length_nil_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_length_nil against the given environment.

list_length_nil_type()

Returns the unelaborated type syntax for theorem list_length_nil.

list_length_singleton_proof()

Returns the unelaborated proof syntax for theorem list_length_singleton.

list_length_singleton_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_length_singleton against the given environment.

list_length_singleton_type()

Returns the unelaborated type syntax for theorem list_length_singleton.

list_length_two_proof()

Returns the unelaborated proof syntax for theorem list_length_two.

list_length_two_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_length_two against the given environment.

list_length_two_type()

Returns the unelaborated type syntax for theorem list_length_two.

list_nil_is_list_proof()

Returns the unelaborated proof syntax for theorem list_nil_is_list.

list_nil_is_list_theorem(env \\ Theoria.new_env())

Elaborates and checks theorem list_nil_is_list against the given environment.

list_nil_is_list_type()

Returns the unelaborated type syntax for theorem list_nil_is_list.