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
Home
Index