### Nuprl Lemma : implies-quotient-true2

`∀[P,Q:ℙ].  ((P `` ⇃(Q)) `` {⇃(P) `` ⇃(Q)})`

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` implies: `P `` Q` true: `True`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` 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` all: `∀x:A. B[x]` true: `True`
Lemmas referenced :  implies-quotient-true quotient_wf true_wf equiv_rel_true equal_wf equal-wf-base quotient-member-eq
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality cumulativity lambdaEquality hypothesis because_Cache independent_isectElimination independent_functionElimination functionEquality universeEquality rename pointwiseFunctionalityForEquality pertypeElimination productElimination equalityTransitivity equalitySymmetry dependent_functionElimination productEquality natural_numberEquality

Latex:
\mforall{}[P,Q:\mBbbP{}].    ((P  {}\mRightarrow{}  \00D9(Q))  {}\mRightarrow{}  \{\00D9(P)  {}\mRightarrow{}  \00D9(Q)\})

Date html generated: 2017_04_14-AM-07_39_57
Last ObjectModification: 2017_02_27-PM-03_11_20

Theory : quot_1

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