Nuprl Lemma : deq_property
∀[T:Type]. ∀[d:EqDecider(T)]. ∀[x,y:T]. uiff(x = y ∈ T;↑(d x y))
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
iff_wf,
all_wf,
bool_wf,
set_wf,
equal_wf,
assert_witness,
decidable__assert,
assert_wf,
sq_stable_from_decidable
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
setElimination,
thin,
rename,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
applyEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
functionEquality,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[d:EqDecider(T)]. \mforall{}[x,y:T]. uiff(x = y;\muparrow{}(d x y))
Date html generated:
2016_05_14-AM-06_06_22
Last ObjectModification:
2016_01_14-PM-07_31_49
Theory : equality!deciders
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