Nuprl Lemma : safe-assert-deq
∀[T:Type]. ∀[d:EqDecider(T)]. ∀[x,y:T]. uiff(↑(eqof(d) x y);x = y ∈ T)
Proof
Definitions occuring in Statement :
eqof: eqof(d),
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 :
eqof: eqof(d),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
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,
sq_stable_from_decidable,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
setElimination,
thin,
rename,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
applyEquality,
hypothesisEquality,
independent_functionElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[d:EqDecider(T)]. \mforall{}[x,y:T]. uiff(\muparrow{}(eqof(d) x y);x = y)
Date html generated:
2016_05_14-AM-06_06_30
Last ObjectModification:
2016_01_14-PM-07_31_50
Theory : equality!deciders
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