Nuprl Lemma : quotient-top-prod-top
⇃(Top × Top) ⊆r (Top × Top)
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
subtype_rel: A ⊆r B,
top: Top,
true: True,
product: x:A × B[x]
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
top: Top,
prop: ℙ,
uall: ∀[x:A]. B[x],
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
top_wf,
true_wf,
equal_wf,
equal-wf-base,
quotient_wf,
equiv_rel_true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
pointwiseFunctionalityForEquality,
productEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
thin,
sqequalHypSubstitution,
sqequalRule,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
because_Cache,
rename,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
independent_isectElimination
Latex:
\00D9(Top \mtimes{} Top) \msubseteq{}r (Top \mtimes{} Top)
Date html generated:
2017_04_14-AM-07_40_06
Last ObjectModification:
2017_02_27-PM-03_11_25
Theory : quot_1
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