### Nuprl Lemma : quotient-bind-ext

`∀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` implies: `P `` Q` cand: `A c∧ B`
Lemmas referenced :  quotient_wf true_wf equiv_rel_true istype-universe quotient-member-eq
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :lambdaFormation_alt,  cut sqequalHypSubstitution hypothesis Error :functionIsType,  Error :universeIsType,  hypothesisEquality introduction extract_by_obid isectElimination thin sqequalRule Error :lambdaEquality_alt,  Error :inhabitedIsType,  independent_isectElimination instantiate universeEquality pointwiseFunctionalityForEquality pertypeElimination productElimination Error :productIsType,  Error :equalityIstype,  sqequalBase equalitySymmetry because_Cache equalityTransitivity applyEquality dependent_functionElimination independent_functionElimination baseApply closedConclusion baseClosed

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

Date html generated: 2019_06_20-PM-00_32_35
Last ObjectModification: 2018_11_24-PM-10_16_15

Theory : quot_1

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