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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