Decomposes a conjunction in the antecedent of a goal.
Decomposes a conjunction in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Decomposes a conjunction in the succedent of a goal.
Decomposes a conjunction in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Performs backwards chaining:
A goal of the form ∀x (P(x) → Q(x)), Γ :- Δ, Q(t)
is replaced by the goal ∀x (P(x) → Q(x)), Γ :- Δ, P(t)
.
Introduces a cut, creating two new subgoals.
Introduces a cut, creating two new subgoals.
The label for the cut formula.
The cut formula.
Attempts to decompose a formula by trying all tactics that don't require additional information.
Attempts to decompose a formula by trying all tactics that don't require additional information.
Note that this tactic only decomposes the outermost symbol, i.e. it only performs one step.
The label of the formula to be decomposed.
Applies an equation in a goal.
Applies an equation in a goal.
The label of the equation.
The label of the formula the equation is to be used on.
If Some(true)
, the equation s = t
will be used to rewrite s
to t
, and the other way around
for Some(false). If None
, the tactic will attempt to decide the direction automatically.
If Some(f)
, the tactic will attempt to produce f
through application of the equality. Otherwise
it will replace as many occurrences as possible according to leftToRight
.
Decomposes an existential quantifier in the antecedent of a goal.
Decomposes an existential quantifier in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
If Some(v), the rule will attempt to use v as the eigenvariable. Otherwise it will automatically pick one.
Decomposes a block of existential quantifiers in the antecedent of a goal.
Decomposes a block of existential quantifiers in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Instantiations for the quantifiers in the block.
Whether the quantified formula should be forgotten after instantiating.
Decomposes a block of universal quantifiers in the succedent of a goal.
Decomposes a block of universal quantifiers in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Instantiations for the quantifiers in the block.
Whether the quantified formula should be forgotten after instantiating.
Decomposes a universal quantifier in the succedent of a goal.
Decomposes a universal quantifier in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
If Some(v), the rule will attempt to use v as the eigenvariable. Otherwise it will automatically pick one.
Decomposes an implication in the antecedent of a goal.
Decomposes an implication in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Decomposes an implication in the succedent of a goal.
Decomposes an implication in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Reduces a subgoal via induction.
Reduces a subgoal via induction.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
A at.logic.gapt.proofs.Context. Used to find the constructors of inductive types.
Inserts an at.logic.gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
Inserts an at.logic.gapt.proofs.lk.LKProof if the insertion sequent subsumes the sequent of the subgoal.
The at.logic.gapt.proofs.lk.LKProof to be inserted. Its end sequent must subsume the current goal.
Decomposes a negation in the antecedent of a goal.
Decomposes a negation in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Decomposes a negation in the succedent of a goal.
Decomposes a negation in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Decomposes a disjunction in the antecedent of a goal.
Decomposes a disjunction in the antecedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Decomposes a disjunction in the succedent of a goal.
Decomposes a disjunction in the succedent of a goal.
How to apply the tactic: To a specific label, to the only fitting formula, or to any fitting formula.
Applies the given Tactical to the proof state until it fails.
Rewrites using the specified equations at the target, either once or as often as possible.
Rewrites using the specified equations at the target, either once or as often as possible.
Universally quantified equations on the antecedent, with direction (left-to-right?)
Formula to rewrite.
Rewrite exactly once?
Removes a formula from the antecedent of a goal.
Removes a formula from the antecedent of a goal.
The label of the formula to be removed.
Removes a formula from the succedent of a goal.
Removes a formula from the succedent of a goal.
The label of the formula to be removed.
Closes a goal of the form ⊥, Γ :- Δ
Repeatedly applies unambiguous unary rules to the entire goal.
Calls Escargot on the subgoal.
Closes a goal of the form A, Γ :- Δ, Δ
Calls the GAPT tableau prover on the subgoal.
Calls prover9 on the subgoal.
Closes a goal of the form Γ :- Δ, s = s
Trivial "unit" tactical.
Closes a goal of the form Γ :- Δ, ⊤