Nuprl Lemma : assert_of_set_leq
∀[p:PosetSig]. ∀[a,b:|p|]. uiff(↑(a (≤b) b);a ≤ b)
Proof
Definitions occuring in Statement :
set_leq: a ≤ b,
set_le: ≤b,
set_car: |p|,
poset_sig: PosetSig,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
infix_ap: x f y
Definitions unfolded in proof :
set_leq: a ≤ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
infix_ap: x f y,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
assert_witness,
set_le_wf,
assert_wf,
set_car_wf,
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:PosetSig]. \mforall{}[a,b:|p|]. uiff(\muparrow{}(a (\mleq{}\msubb{}) b);a \mleq{} b)
Date html generated:
2016_05_15-PM-00_04_13
Last ObjectModification:
2015_12_26-PM-11_28_44
Theory : sets_1
Home
Index