Nuprl Lemma : qoset_lt_trans
∀[s:QOSet]. ∀[a,b,c:|s|]. (a <s c) supposing ((b <s c) and (a <s b))
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_lt: a <p b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
utrans: UniformlyTrans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
qoset: QOSet,
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
strict_part: strict_part(x,y.R[x; y];a;b),
set_leq: a ≤ b,
infix_ap: x f y,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
set_lt: a <p b,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
utrans_functionality_wrt_iff,
set_car_wf,
set_lt_wf,
strict_part_wf,
set_leq_wf,
iff_weakening_uiff,
set_lt_is_sp_of_leq,
assert_witness,
set_le_wf,
set_blt_wf,
qoset_wf,
utrans_imp_sp_utrans,
set_leq_trans
Rules used in proof :
cut,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
independent_functionElimination,
productElimination,
independent_pairEquality,
dependent_functionElimination,
applyEquality,
isect_memberEquality,
voidElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[s:QOSet]. \mforall{}[a,b,c:|s|]. (a <s c) supposing ((b <s c) and (a <s b))
Date html generated:
2016_05_15-PM-00_04_45
Last ObjectModification:
2015_12_26-PM-11_28_26
Theory : sets_1
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