Nuprl Lemma : no-excluded-middle-quot-true1
¬(∀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,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
true: True,
member: t ∈ T,
squash: ↓T,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
sym: Sym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_apply: x[s1;s2],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
istype-base,
has-value_wf_base,
istype-void,
squash_wf,
true_wf,
not-has-value-decidable-quot,
all_wf,
base_wf,
quotient_wf,
or_wf,
not_wf,
equiv_rel_true,
quotient-dep-function-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
independent_pairFormation,
introduction,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
sqequalHypSubstitution,
hypothesis,
imageElimination,
extract_by_obid,
Error :functionIsType,
Error :unionIsType,
Error :universeIsType,
isectElimination,
because_Cache,
Error :inhabitedIsType,
Error :lambdaEquality_alt,
closedConclusion,
independent_isectElimination,
universeEquality,
dependent_functionElimination,
rename,
independent_functionElimination,
voidElimination,
applyEquality
Latex:
\mneg{}(\mforall{}P:\mBbbP{}. \00D9(P \mvee{} (\mneg{}P)))
Date html generated:
2019_06_20-PM-00_32_39
Last ObjectModification:
2018_10_16-PM-02_41_49
Theory : quot_1
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