### Nuprl Lemma : or-quotient-true-subtype

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

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` subtype_rel: `A ⊆r B` prop: `ℙ` all: `∀x:A. B[x]` not: `¬A` or: `P ∨ Q` true: `True`
Definitions unfolded in proof :  all: `∀x:A. B[x]` or: `P ∨ Q` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` and: `P ∧ Q` false: `False` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]`
Lemmas referenced :  disjoint-quotient_subtype not_wf and_wf true_wf equiv_rel_true
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation sqequalRule cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_isectElimination productElimination independent_functionElimination voidElimination lambdaEquality unionEquality universeEquality

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

Date html generated: 2016_05_14-AM-06_08_53
Last ObjectModification: 2015_12_26-AM-11_48_11

Theory : quot_1

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