Nuprl Lemma : set_leq_weakening_lt
∀[s:QOSet]. ∀[a,b:|s|]. a ≤ b supposing a <s b
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_lt: a <p b,
set_leq: a ≤ b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
set_leq: a ≤ b,
infix_ap: x f y,
qoset: QOSet,
dset: DSet,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
strict_part: strict_part(x,y.R[x; y];a;b)
Lemmas referenced :
assert_witness,
set_le_wf,
set_lt_wf,
set_car_wf,
qoset_wf,
set_lt_is_sp_of_leq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination
Latex:
\mforall{}[s:QOSet]. \mforall{}[a,b:|s|]. a \mleq{} b supposing a <s b
Date html generated:
2019_10_15-AM-10_32_28
Last ObjectModification:
2018_08_22-AM-09_39_18
Theory : sets_1
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