37 lines
1 KiB
Text
37 lines
1 KiB
Text
import logic data.prod
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open tactic prod
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inductive inh [class] (A : Type) : Prop :=
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intro : A -> inh A
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instance inh.intro
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theorem inh_elim {A : Type} {B : Prop} (H1 : inh A) (H2 : A → B) : B
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:= inh.rec H2 H1
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theorem inh_exists {A : Type} {P : A → Prop} (H : ∃x, P x) : inh A
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:= obtain w Hw, from H, inh.intro w
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theorem inh_bool [instance] : inh Prop
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:= inh.intro true
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theorem inh_fun [instance] {A B : Type} (H : inh B) : inh (A → B)
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:= inh.rec (λb, inh.intro (λa : A, b)) H
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theorem pair_inh [instance] {A : Type} {B : Type} (H1 : inh A) (H2 : inh B) : inh (prod A B)
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:= inh_elim H1 (λa, inh_elim H2 (λb, inh.intro (pair a b)))
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definition assump := eassumption
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tactic_hint assump
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theorem tst {A B : Type} (H : inh B) : inh (A → B → B)
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set_option elaborator.trace_instances true
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theorem T1 {A B C D : Type} {P : C → Prop} (a : A) (H1 : inh B) (H2 : ∃x, P x) : inh ((A → A) × B × (D → C) × Prop) :=
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have h1 [visible] : inh A, from inh.intro a,
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have h2 [visible] : inh C, from inh_exists H2,
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_
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(*
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print(get_env():find("T1"):value())
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*)
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