Nuprl Lemma : comparison-seq-simple-wf
∀[T:Type]. ∀[c1,c2:comparison(T)]. (comparison-seq(c1; c2) ∈ comparison(T))
Proof
Definitions occuring in Statement :
comparison-seq: comparison-seq(c1; c2),
comparison: comparison(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
comparison: comparison(T),
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
comparison-seq_wf,
subtype_rel_comparison,
equal-wf-T-base,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
applyEquality,
setEquality,
intEquality,
setElimination,
rename,
hypothesis,
baseClosed,
independent_isectElimination,
lambdaEquality,
because_Cache,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[c1,c2:comparison(T)]. (comparison-seq(c1; c2) \mmember{} comparison(T))
Date html generated:
2017_04_17-AM-08_28_22
Last ObjectModification:
2017_02_27-PM-04_49_29
Theory : list_1
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