Folding tactics
These tactic definitions can be used to fold multiple instances of negations:
{{{#!coq Tactic Notation "fold" "any" "not" := repeat ( match goal with | |- context [?P -> False] => fold (~ P) end).
Tactic Notation "fold" "any" "not" "in" ident(H) "|-" := repeat ( match goal with | J: context [?P -> False] |- _ => fold (~ P) in H end).
Tactic Notation "fold" "any" "not" "in" ident(H) := fold any not in H |-.
Tactic Notation "fold" "any" "not" "in" "*" "|-" := repeat ( match goal with | H: context [?P -> False] |- _ => fold (~ P) in H end).
Tactic Notation "fold" "any" "not" "in" "*" := fold any not in * |-; fold any not.
Tactic Notation "fold" "any" "not" "in" "" "|-" "" := fold any not in *. }}}
Similarly, these tactics can be uses to fold logical equivalences:
{{{#!coq Tactic Notation "fold" "any" "iff" := repeat ( match goal with | |- context [(?P -> ?Q) /\ (?Q -> ?P)] => fold (P <-> Q) end).
Tactic Notation "fold" "any" "iff" "in" ident(H) "|-" := repeat ( match goal with | J: context [(?P -> ?Q) /\ (?Q -> ?P)] |- _ => fold (P <-> Q) in H end).
Tactic Notation "fold" "any" "iff" "in" ident(H) := fold any iff in H |-.
Tactic Notation "fold" "any" "iff" "in" "*" "|-" := repeat ( match goal with | H: context [(?P -> ?Q) /\ (?Q -> ?P)] |- _ => fold (P <-> Q) in H end).
Tactic Notation "fold" "any" "iff" "in" "*" := fold any iff in * |-; fold any iff.
Tactic Notation "fold" "any" "iff" "in" "" "|-" "" := fold any iff in *. }}}
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