Nuprl Lemma : not-quotient-true
∀[P:ℙ]. (¬⇃(P) ⇐⇒ ¬P)
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
not: ¬A,
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
rev_implies: P ⇐ Q,
quotient: x,y:A//B[x; y],
cand: A c∧ B
Lemmas referenced :
trivial-quotient-true,
istype-universe,
not_wf,
quotient_wf,
true_wf,
equiv_rel_true,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
Error :lambdaFormation_alt,
thin,
sqequalHypSubstitution,
independent_functionElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
voidElimination,
Error :universeIsType,
cumulativity,
sqequalRule,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
independent_isectElimination,
because_Cache,
productElimination,
independent_pairEquality,
dependent_functionElimination,
Error :functionIsTypeImplies,
universeEquality,
pointwiseFunctionality,
pertypeElimination,
Error :productIsType,
Error :equalityIsType4,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[P:\mBbbP{}]. (\mneg{}\00D9(P) \mLeftarrow{}{}\mRightarrow{} \mneg{}P)
Date html generated:
2019_06_20-PM-00_32_37
Last ObjectModification:
2018_10_06-PM-04_17_45
Theory : quot_1
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