Nuprl Lemma : trivial-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,
implies: P ⇒ Q,
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
true_wf,
equiv_rel_true,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
rename,
introduction,
hypothesisEquality,
universeEquality,
sqequalHypSubstitution,
lambdaEquality,
cut,
lemma_by_obid,
hypothesis,
sqequalRule,
isectElimination,
thin,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[P:\mBbbP{}]. (P {}\mRightarrow{} \00D9(P))
Date html generated:
2016_05_14-AM-06_08_41
Last ObjectModification:
2015_12_26-AM-11_48_16
Theory : quot_1
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