Nuprl Lemma : no-excluded-middle-squash-using-partial
¬↓∀P:ℙ. (P ∨ (¬P))
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
squash: ↓T,
or: P ∨ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
squash: ↓T,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
or: P ∨ Q,
all: ∀x:A. B[x]
Lemmas referenced :
no-excluded-middle-using-partial,
squash_wf,
all_wf,
or_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
imageElimination,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
Error :universeIsType,
instantiate,
isectElimination,
closedConclusion,
universeEquality,
sqequalRule,
Error :lambdaEquality_alt,
hypothesisEquality,
because_Cache,
applyEquality,
cumulativity,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry
Latex:
\mneg{}\mdownarrow{}\mforall{}P:\mBbbP{}. (P \mvee{} (\mneg{}P))
Date html generated:
2019_06_20-PM-00_34_57
Last ObjectModification:
2018_10_15-PM-03_55_20
Theory : partial_1
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