Nuprl Lemma : decidable__atom_equal_1
∀a,b:Atom1. Dec(a = b ∈ Atom1)
Proof
Definitions occuring in Statement :
atom: Atom$n,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
decidable: Dec(P),
member: t ∈ T,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
guard: {T}
Lemmas referenced :
not_wf,
equal-wf-base,
atom1_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
atomnEquality,
introduction,
atomn_eqEquality,
hypothesisEquality,
inlEquality,
axiomEquality,
hypothesis,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
sqequalRule,
inrEquality,
lambdaEquality,
because_Cache,
voidElimination,
independent_functionElimination
Latex:
\mforall{}a,b:Atom1. Dec(a = b)
Date html generated:
2019_06_20-AM-11_20_16
Last ObjectModification:
2018_08_07-PM-05_52_20
Theory : atom_1
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