Nuprl - Proof: dec iff ex bvfun 1 1 1 1 1 1 1 1

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At: dec iff ex bvfun 1 1 1 1 1 1 1 1

1. T : Type
2. E : T

T

Prop
3. g : x:T

y:T. E(x,y)

E(x,y)
4. x : T
5. y : T
6. y1 : y:T

E(x,y)

E(x,y)
7. y1 = g(x)
8. x1 : E(x,y)
9. inl(x1) = g(x,y)

InjCase(inl(x1); a. true

; b. false

)

E(x,y)

By:

Reduce 0

Generated subgoal:

1 True E(x,y)
Auto

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