Nuprl Lemma : eqof_equal_btrue
∀[A:Type]. ∀[d:EqDecider(A)]. ∀[i,j:A]. eqof(d) i j ~ tt supposing i = j ∈ A
Proof
Definitions occuring in Statement :
eqof: eqof(d),
deq: EqDecider(T),
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
eqof_wf,
btrue_wf,
equal_wf,
true_wf,
safe-assert-deq,
assert_wf,
iff_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
applyEquality,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
addLevel,
productElimination,
impliesFunctionality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[d:EqDecider(A)]. \mforall{}[i,j:A]. eqof(d) i j \msim{} tt supposing i = j
Date html generated:
2016_05_14-AM-06_06_45
Last ObjectModification:
2015_12_26-AM-11_46_42
Theory : equality!deciders
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