### Nuprl Lemma : or-quotient-true

`∀P:ℙ. (⇃(P ∨ (¬P)) `` (⇃(P) ∨ ⇃(¬P)))`

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` prop: `ℙ` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` or: `P ∨ Q` true: `True`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` uimplies: `b supposing a` or: `P ∨ Q` quotient: `x,y:A//B[x; y]` and: `P ∧ Q` not: `¬A` false: `False` true: `True`
Lemmas referenced :  or_wf quotient_wf true_wf equiv_rel_true not_wf quotient-member-eq equal_wf equal-wf-base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation rename introduction pointwiseFunctionalityForEquality cut lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality sqequalRule lambdaEquality hypothesis because_Cache independent_isectElimination pertypeElimination productElimination equalityTransitivity equalitySymmetry unionElimination inlEquality dependent_functionElimination independent_functionElimination voidElimination inrEquality natural_numberEquality productEquality universeEquality

Latex:
\mforall{}P:\mBbbP{}.  (\00D9(P  \mvee{}  (\mneg{}P))  {}\mRightarrow{}  (\00D9(P)  \mvee{}  \00D9(\mneg{}P)))

Date html generated: 2016_05_14-AM-06_08_36
Last ObjectModification: 2015_12_26-AM-11_48_17

Theory : quot_1

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