Nuprl Lemma : deq_functionality_wrt_ext-eq
∀[A,B:Type]. EqDecider(A) ≡ EqDecider(B) supposing A ≡ B
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
subtype_rel_dep_function,
bool_wf,
subtype_rel_self,
equal_wf,
equal_functionality_wrt_subtype_rel2,
assert_wf,
all_wf,
iff_wf,
deq_wf,
ext-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
lemma_by_obid,
isectElimination,
sqequalRule,
functionEquality,
hypothesis,
independent_isectElimination,
lambdaFormation,
because_Cache,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. EqDecider(A) \mequiv{} EqDecider(B) supposing A \mequiv{} B
Date html generated:
2016_05_14-AM-06_06_20
Last ObjectModification:
2015_12_26-AM-11_46_57
Theory : equality!deciders
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