Nuprl Lemma : quotient-bind
∀A,B:Type. (⇃(A) ⇒ (A ⇒ ⇃(B)) ⇒ ⇃(B))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
guard: {T},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
equiv_rel_true,
true_wf,
quotient_wf,
implies-quotient-true2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
functionEquality,
cumulativity,
sqequalRule,
lambdaEquality,
because_Cache,
independent_isectElimination,
universeEquality
Latex:
\mforall{}A,B:Type. (\00D9(A) {}\mRightarrow{} (A {}\mRightarrow{} \00D9(B)) {}\mRightarrow{} \00D9(B))
Date html generated:
2016_05_14-AM-06_08_42
Last ObjectModification:
2016_05_13-AM-03_17_50
Theory : quot_1
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