### Nuprl Lemma : quotient-bind-ext2

`∀A,B:Type. ∀a:⇃(A). ∀f:A ⟶ ⇃(B).  (f a ∈ ⇃(B))`

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` all: `∀x:A. B[x]` true: `True` member: `t ∈ T` apply: `f a` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` uimplies: `b supposing a` quotient: `x,y:A//B[x; y]` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  eq-in-quot equal-wf-base equiv_rel_true true_wf quotient_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalHypSubstitution hypothesis functionEquality cumulativity hypothesisEquality lemma_by_obid isectElimination thin sqequalRule lambdaEquality because_Cache independent_isectElimination universeEquality pointwiseFunctionalityForEquality pertypeElimination productElimination productEquality applyEquality functionExtensionality dependent_functionElimination equalityTransitivity equalitySymmetry

Latex:
\mforall{}A,B:Type.  \mforall{}a:\00D9(A).  \mforall{}f:A  {}\mrightarrow{}  \00D9(B).    (f  a  \mmember{}  \00D9(B))

Date html generated: 2016_05_14-AM-06_08_48
Last ObjectModification: 2016_05_13-PM-00_10_06

Theory : quot_1

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