# Documentation

Std.Tactic.Basic

exfalso converts a goal ⊢ tgt into ⊢ False by applying False.elim.

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_ in tactic position acts like the done tactic: it fails and gives the list of goals if there are any. It is useful as a placeholder after starting a tactic block such as by _ to make it syntactically correct and show the current goal.

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fail_if_success t fails if the tactic t succeeds.

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rwa calls rw, then closes any remaining goals using assumption.

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Like exact, but takes a list of terms and checks that all goals are discharged after the tactic.

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by_contra h proves ⊢ p by contradiction, introducing a hypothesis h : ¬p and proving False.

• If p is a negation ¬q, h : q will be introduced instead of ¬¬q.
• If p is decidable, it uses Decidable.byContradiction instead of Classical.byContradiction.
• If h is omitted, the introduced variable _: ¬p will be anonymous.
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iterate n tac runs tac exactly n times. iterate tac runs tac repeatedly until failure.

To run multiple tactics, one can do iterate (tac₁; tac₂; ⋯) or

iterate
tac₁
tac₂
⋯

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repeat' tac runs tac on all of the goals to produce a new list of goals, then runs tac again on all of those goals, and repeats until tac fails on all remaining goals.

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repeat1 tac applies tac to main goal at least once. If the application succeeds, the tactic is applied recursively to the generated subgoals until it eventually fails.

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subst_eqs applies subst to all equalities in the context as long as it makes progress.

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split_ands applies And.intro until it does not make progress.

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fapply e is like apply e but it adds goals in the order they appear, rather than putting the dependent goals first.

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eapply e is like apply e but it does not add subgoals for variables that appear in the types of other goals. Note that this can lead to a failure where there are no goals remaining but there are still metavariables in the term:

example (h : ∀ x : Nat, x = x → True) : True := by
eapply h
rfl
-- no goals
-- (kernel) declaration has metavariables '_example'

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Tries to solve the goal using a canonical proof of True, or the rfl tactic. Unlike trivial or trivial', does not use the contradiction tactic.

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conv tactic to close a goal using an equality theorem.

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