Nuprl Lemma : no-excluded-middle-quot-true2
¬(∀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,
or: P ∨ Q,
true: True
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
has-value: (a)↓,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
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,
true: True,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
bottom-sqle,
not_id_sqeq_bottom,
equal-wf-base,
equal_wf,
false_wf,
sqle_wf_base,
not_wf,
equiv_rel_true,
true_wf,
quotient_wf,
or_wf,
or-quotient-true-subtype,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
rename,
cut,
sqleRule,
sqleReflexivity,
divergentSqle,
lemma_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
isectElimination,
baseClosed,
sqequalRule,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
because_Cache,
independent_isectElimination,
unionElimination,
introduction,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
productEquality,
sqequalSqle,
isect_memberEquality,
voidEquality,
instantiate,
universeEquality,
cumulativity
Latex:
\mneg{}(\mforall{}P:\mBbbP{}. \00D9(P \mvee{} (\mneg{}P)))
Date html generated:
2016_05_14-AM-06_09_03
Last ObjectModification:
2016_01_14-PM-07_33_22
Theory : quot_1
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