# Basic tactics and utilities for tactic writing #

This file defines some basic utilities for tactic writing, and also

• the introv tactic, which allows the user to automatically introduce the variables of a theorem and explicitly name the non-dependent hypotheses,
• an assumption macro, calling the assumption tactic on all goals
• the tactics match_target, clear_aux_decl (clearing all auxiliary declarations from the context) and clear_value (which clears the bodies of given local definitions, changing them into regular hypotheses).
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def Mathlib.Tactic.pushFVarAliasInfo {m : } [] (oldFVars : ) (newFVars : ) (newLCtx : Lean.LocalContext) :

Given two arrays of FVarIds, one from an old local context and the other from a new local context, pushes FVarAliasInfos into the info tree for corresponding pairs of FVarIds. Recall that variables linked this way should be considered to be semantically identical.

The effect of this is, for example, the unused variable linter will see that variables from the first array are used if corresponding variables in the second array are used.

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The tactic introv allows the user to automatically introduce the variables of a theorem and explicitly name the non-dependent hypotheses. Any dependent hypotheses are assigned their default names.

Examples:

example : ∀ a b : Nat, a = b → b = a := by
introv h,
exact h.symm


The state after introv h is

a b : ℕ,
h : a = b
⊢ b = a

example : ∀ a b : Nat, a = b → ∀ c, b = c → a = c := by
introv h₁ h₂,
exact h₁.trans h₂


The state after introv h₁ h₂ is

a b : ℕ,
h₁ : a = b,
c : ℕ,
h₂ : b = c
⊢ a = c

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Try calling assumption on all goals; succeeds if it closes at least one goal.

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This tactic clears all auxiliary declarations from the context.

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def Lean.MVarId.clearValue (mvarId : Lean.MVarId) (fvarId : Lean.FVarId) :

Clears the value of the local definition fvarId. Ensures that the resulting goal state is still type correct. Throws an error if it is a local hypothesis without a value.

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clear_value n₁ n₂ ... clears the bodies of the local definitions n₁, n₂ ..., changing them into regular hypotheses. A hypothesis n : α := t is changed to n : α.

The order of n₁ n₂ ... does not matter, and values will be cleared in reverse order of where they appear in the context.

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