Nuprl Lemma : decidable__equal_Id
∀a,b:Id. Dec(a = b ∈ Id)
Proof
Definitions occuring in Statement :
Id: Id,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
Id_wf,
assert_wf,
eq_id_wf,
all_wf,
decidable_wf,
decidable_functionality,
iff_weakening_uiff,
assert-eq-id,
decidable__assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
sqequalRule,
lambdaEquality,
addLevel,
allFunctionality,
independent_functionElimination,
productElimination,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination
Latex:
\mforall{}a,b:Id. Dec(a = b)
Date html generated:
2016_05_14-PM-03_37_24
Last ObjectModification:
2015_12_26-PM-05_58_48
Theory : decidable!equality
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