Nuprl Lemma : setsubset_transitivity
∀a,b,c:coSet{i:l}. ((a ⊆ b) ⇒ (b ⊆ c) ⇒ (a ⊆ c))
Proof
Definitions occuring in Statement :
setsubset: (a ⊆ b),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
setsubset_wf,
setsubset-iff,
coSet_wf,
all_wf,
setmem_wf
Rules used in proof :
independent_functionElimination,
productElimination,
dependent_functionElimination,
impliesFunctionality,
addLevel,
functionEquality,
cumulativity,
lambdaEquality,
sqequalRule,
instantiate,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a,b,c:coSet\{i:l\}. ((a \msubseteq{} b) {}\mRightarrow{} (b \msubseteq{} c) {}\mRightarrow{} (a \msubseteq{} c))
Date html generated:
2018_07_29-AM-10_01_26
Last ObjectModification:
2018_07_18-PM-01_30_38
Theory : constructive!set!theory
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