Unfold definitions commonly used in well founded relation definitions.
Since Lean 4.12, Lean unfolds these definitions automatically before presenting the goal to the
user, and this tactic should no longer be necessary. Calls to simp_wf can be removed or replaced
by plain calls to simp.
Equations
- tacticSimp_wf = Lean.ParserDescr.node `tacticSimp_wf 1024 (Lean.ParserDescr.nonReservedSymbol "simp_wf" false)
Instances For
This tactic is used internally by lean before presenting the proof obligations from a well-founded
definition to the user via decreasing_by. It is not necessary to use this tactic manually.
Instances For
Extensible helper tactic for decreasing_tactic. This handles the "base case"
reasoning after applying lexicographic order lemmas.
It can be extended by adding more macro definitions, e.g.
macro_rules | `(tactic| decreasing_trivial) => `(tactic| linarith)
Equations
- tacticDecreasing_trivial = Lean.ParserDescr.node `tacticDecreasing_trivial 1024 (Lean.ParserDescr.nonReservedSymbol "decreasing_trivial" false)
Instances For
Variant of decreasing_trivial that does not use omega, intended to be used in core modules
before omega is available.
Equations
- tacticDecreasing_trivial_pre_omega = Lean.ParserDescr.node `tacticDecreasing_trivial_pre_omega 1024 (Lean.ParserDescr.nonReservedSymbol "decreasing_trivial_pre_omega" false)
Instances For
Constructs a proof of decreasing along a well founded relation, by simplifying, then applying
lexicographic order lemmas and finally using ts to solve the base case. If it fails,
it prints a message to help the user diagnose an ill-founded recursive definition.
Instances For
decreasing_tactic is called by default on well-founded recursions in order
to synthesize a proof that recursive calls decrease along the selected
well founded relation. It can be locally overridden by using decreasing_by tac
on the recursive definition, and it can also be globally extended by adding
more definitions for decreasing_tactic (or decreasing_trivial,
which this tactic calls).