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lean4-htt/tests/lean/815b.lean.expected.out
Kyle Miller 407a59d697
feat: pretty print props with → only if domain is prop, add pp.foralls (#7812) 
This PR modifies the pretty printing of pi types. Now `∀` will be
preferred over `→` for propositions if the domain is not a proposition.
For example, `∀ (n : Nat), True` pretty prints as `∀ (n : Nat), True`
rather than as `Nat → True`. There is also now an option `pp.foralls`
(default true) that when false disables using `∀` at all, for
pedagogical purposes. This PR also adjusts instance implicit binder
pretty printing — nondependent pi types won't show the instance binder
name. Closes #1834.

The linked RFC also suggests using `_` for binder names in case of
non-dependance. We're tabling that idea. Potentially it is useful for
hygienic names; this could improve how `Nat → True` pretty prints as `∀
(a : Nat), True`, with this `a` that's chosen by implication notation
elaboration. Relatedly, this PR exposes even further the issue where
binder names are reused in a confusing way. Consider: `Nat → Nat → (a :
Nat) → a = a` pretty prints as `∀ (a a a : Nat), a = a`.
2025-04-04 02:55:47 +00:00

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815b.lean:1:4-1:13: warning: declaration uses 'sorry'
815b.lean:6:9-6:17: warning: declaration uses 'sorry'
815b.lean:7:9-7:14: warning: declaration uses 'sorry'
815b.lean:8:9-8:13: warning: declaration uses 'sorry'
815b.lean:9:9-9:13: warning: declaration uses 'sorry'
815b.lean:10:9-10:13: warning: declaration uses 'sorry'
815b.lean:11:9-11:13: warning: declaration uses 'sorry'
[Meta.synthInstance] ✅️ IsSmooth fun g a => f (g a) d
[Meta.synthInstance] new goal IsSmooth fun g a => f (g a) d
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, @swap, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to IsSmooth fun g a => f (g a) d
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g a => f (g a) d ≟ IsSmooth f
[Meta.synthInstance] ✅️ apply @swap to IsSmooth fun g a => f (g a) d
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g a => f (g a) d ≟ IsSmooth fun b a => f (b a) d
[Meta.synthInstance] new goal ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a) d ≟ IsSmooth f
[Meta.synthInstance] ✅️ apply @diag to ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a) d ≟ IsSmooth fun a_1 => f (a_1 a) d
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth f
has unused arguments, reduced type
IsSmooth f
Transformer
fun redf a => redf
[Meta.synthInstance] new goal IsSmooth f
[Meta.synthInstance.instances] #[inst✝]
[Meta.synthInstance] ✅️ apply inst✝ to IsSmooth f
[Meta.synthInstance.tryResolve] ✅️ IsSmooth f ≟ IsSmooth f
[Meta.synthInstance.answer] ✅️ IsSmooth f
[Meta.synthInstance.resume] propagating IsSmooth f to subgoal IsSmooth f of ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.resume] size: 1
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth f
has unused arguments, reduced type
IsSmooth f
Transformer
fun redf a => redf
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth f to subgoal ∀ (a : α), IsSmooth f of ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.resume] size: 2
[Meta.synthInstance.unusedArgs] ∀ (a : α) (b : β), IsSmooth (f b)
has unused arguments, reduced type
∀ (b : β), IsSmooth (f b)
Transformer
fun redf a => redf
[Meta.synthInstance] new goal ∀ (b : β), IsSmooth (f b)
[Meta.synthInstance.instances] #[inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to ∀ (b : β), IsSmooth (f b)
[Meta.synthInstance.tryResolve] ❌️ IsSmooth (f b) ≟ IsSmooth f
[Meta.synthInstance] ❌️ apply @comp to ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a) d ≟ IsSmooth fun a_1 => ?m a (?m a a_1)
[Meta.synthInstance] ✅️ apply @parm to ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a) d ≟ IsSmooth fun a_1 => f (a_1 a) d
[Meta.synthInstance] new goal ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, @swap, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a) ≟ IsSmooth f
[Meta.synthInstance] ✅️ apply @swap to ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a) ≟ IsSmooth fun b a_1 => f (b a) a_1
[Meta.synthInstance] new goal ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a✝) a ≟ IsSmooth f
[Meta.synthInstance] ✅️ apply @diag to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a✝) a ≟ IsSmooth fun a_1 => f (a_1 a✝) a
[Meta.synthInstance.unusedArgs] ∀ (a : α) (a : δ), IsSmooth f
has unused arguments, reduced type
IsSmooth f
Transformer
fun redf a a => redf
[Meta.synthInstance.resume] propagating ∀ (a : α) (a : δ),
IsSmooth f to subgoal ∀ (a : α) (a : δ), IsSmooth f of ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.resume] size: 1
[Meta.synthInstance.unusedArgs] ∀ (a : α) (a : δ) (b : β), IsSmooth (f b)
has unused arguments, reduced type
∀ (b : β), IsSmooth (f b)
Transformer
fun redf a a => redf
[Meta.synthInstance] ❌️ apply @comp to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g =>
f (g a✝) a ≟ IsSmooth fun a_1 => ?m a✝ a (?m a✝ a a_1)
[Meta.synthInstance] ✅️ apply @parm to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a✝) a ≟ IsSmooth fun a_1 => f (a_1 a✝) a
[Meta.synthInstance.unusedArgs] ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a)
has unused arguments, reduced type
∀ (a : α), IsSmooth fun g => f (g a)
Transformer
fun redf a a_1 => redf a
[Meta.synthInstance] ❌️ apply @const to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a✝) a ≟ IsSmooth fun a_1 => ?m a✝ a
[Meta.synthInstance] ❌️ apply @identity to ∀ (a : α) (a_1 : δ), IsSmooth fun g => f (g a) a_1
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => f (g a✝) a ≟ IsSmooth fun a => a
[Meta.synthInstance] ❌️ apply @diag to ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g =>
f (g a) ≟ IsSmooth fun a_1 => ?m a (?m a a_1) (?m a a_1)
[Meta.synthInstance] ✅️ apply @comp to ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => f (g a) ≟ IsSmooth fun a_1 => f (a_1 a)
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth f
has unused arguments, reduced type
IsSmooth f
Transformer
fun redf a => redf
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth f to subgoal ∀ (a : α), IsSmooth f of ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.resume] size: 1
[Meta.synthInstance] new goal ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g a ≟ IsSmooth f
[Meta.synthInstance] ❌️ apply @diag to ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g =>
g a ≟ IsSmooth fun a_1 => ?m a (?m a a_1) (?m a a_1)
[Meta.synthInstance] ❌️ apply @comp to ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g a ≟ IsSmooth fun a_1 => ?m a (?m a a_1)
[Meta.synthInstance] ✅️ apply @parm to ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => g a ≟ IsSmooth fun a_1 => a_1 a
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth fun g => g
has unused arguments, reduced type
IsSmooth fun g => g
Transformer
fun redf a => redf
[Meta.synthInstance] new goal IsSmooth fun g => g
[Meta.synthInstance.instances] #[@identity, @const, @parm, @comp, @diag, @swap, inst✝]
[Meta.synthInstance] ❌️ apply inst✝ to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g ≟ IsSmooth f
[Meta.synthInstance] ✅️ apply @swap to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => g ≟ IsSmooth fun b a => b a
[Meta.synthInstance] ❌️ apply @diag to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g ≟ IsSmooth fun a => ?m (?m a) (?m a)
[Meta.synthInstance] ❌️ apply @comp to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g ≟ IsSmooth fun a => ?m (?m a)
[Meta.synthInstance] ❌️ apply @parm to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g ≟ IsSmooth fun a => ?m a ?m
[Meta.synthInstance] ❌️ apply @const to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ❌️ IsSmooth fun g => g ≟ IsSmooth fun a => ?m
[Meta.synthInstance] ✅️ apply @identity to IsSmooth fun g => g
[Meta.synthInstance.tryResolve] ✅️ IsSmooth fun g => g ≟ IsSmooth fun a => a
[Meta.synthInstance.answer] ✅️ IsSmooth fun g => g
[Meta.synthInstance.resume] propagating IsSmooth fun a =>
a to subgoal IsSmooth fun g => g of ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] size: 1
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth fun g => g
has unused arguments, reduced type
IsSmooth fun g => g
Transformer
fun redf a => redf
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a => a to subgoal ∀ (a : α), IsSmooth fun g => g of ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] size: 2
[Meta.synthInstance.answer] ✅️ ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a_1 => a_1 a to subgoal ∀ (a : α), IsSmooth fun g => g a of IsSmooth fun g => g
[Meta.synthInstance.resume] size: 3
[Meta.synthInstance.answer] ✅️ IsSmooth fun g => g
[Meta.synthInstance.resume] propagating IsSmooth fun b a =>
b a to subgoal IsSmooth fun g => g of ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] size: 4
[Meta.synthInstance.unusedArgs] ∀ (a : α), IsSmooth fun g => g
has unused arguments, reduced type
IsSmooth fun g => g
Transformer
fun redf a => redf
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun b a => b a to subgoal ∀ (a : α), IsSmooth fun g => g of ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] size: 8
[Meta.synthInstance.answer] ✅️ ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a => a to subgoal ∀ (a : α), IsSmooth fun g => g of ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] size: 5
[Meta.synthInstance.answer] ✅️ ∀ (a : α), IsSmooth fun g => g a
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a_1 => a_1 a to subgoal ∀ (a : α), IsSmooth fun g => g a of ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.resume] size: 4
[Meta.synthInstance.answer] ✅️ ∀ (a : α), IsSmooth fun g => f (g a)
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a_1 =>
f (a_1 a) to subgoal ∀ (a : α), IsSmooth fun g => f (g a) of ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.resume] size: 5
[Meta.synthInstance.answer] ✅️ ∀ (a : α), IsSmooth fun g => f (g a) d
[Meta.synthInstance.resume] propagating ∀ (a : α),
IsSmooth fun a_1 =>
f (a_1 a) d to subgoal ∀ (a : α), IsSmooth fun g => f (g a) d of IsSmooth fun g a => f (g a) d
[Meta.synthInstance.resume] size: 6
[Meta.synthInstance.answer] ✅️ IsSmooth fun g a => f (g a) d
[Meta.synthInstance] result swap fun a g => f (g a) d
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