Nuprl Lemma : subtype_rel_comparison
∀[A,B:Type]. comparison(B) ⊆r comparison(A) supposing A ⊆r B
Proof
Definitions occuring in Statement :
comparison: comparison(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
comparison: comparison(T),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
subtype_rel_dep_function,
subtype_rel_self,
equal_wf,
iff_weakening_equal,
equal-wf-T-base,
le_wf,
all_wf,
comparison_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
sqequalRule,
functionEquality,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
lambdaFormation,
because_Cache,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
minusEquality,
functionExtensionality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
independent_pairFormation,
natural_numberEquality,
productEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. comparison(B) \msubseteq{}r comparison(A) supposing A \msubseteq{}r B
Date html generated:
2017_04_17-AM-08_26_22
Last ObjectModification:
2017_02_27-PM-04_48_03
Theory : list_1
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