Nuprl Lemma : assert-eq-id
∀[a,b:Id]. uiff(↑a = b;a = b ∈ Id)
Proof
Definitions occuring in Statement :
eq_id: a = b,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eq_id: a = b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
eqof: eqof(d)
Lemmas referenced :
id-deq_wf,
deq_wf,
Id_wf,
equal_wf,
iff_weakening_uiff,
assert_wf,
eqof_wf,
safe-assert-deq,
assert_witness,
uiff_wf,
eq_id_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
hypothesis,
thin,
sqequalHypSubstitution,
isectElimination,
lambdaFormation,
independent_pairFormation,
hypothesisEquality,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
applyEquality,
independent_functionElimination,
cumulativity,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[a,b:Id]. uiff(\muparrow{}a = b;a = b)
Date html generated:
2017_04_17-AM-09_18_34
Last ObjectModification:
2017_02_27-PM-05_22_08
Theory : decidable!equality
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