Nuprl Lemma : set_lt_is_sp_of_leq_a
∀[p:PosetSig]. ∀[a,b:|p|]. uiff(a <p b;(a ≤ b) ∧ (¬(b ≤ a)))
Proof
Definitions occuring in Statement :
set_lt: a <p b,
set_leq: a ≤ b,
set_car: |p|,
poset_sig: PosetSig,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q
Definitions unfolded in proof :
strict_part: strict_part(x,y.R[x; y];a;b)
Lemmas referenced :
set_lt_is_sp_of_leq
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[p:PosetSig]. \mforall{}[a,b:|p|]. uiff(a <p b;(a \mleq{} b) \mwedge{} (\mneg{}(b \mleq{} a)))
Date html generated:
2016_05_15-PM-00_04_24
Last ObjectModification:
2015_12_26-PM-11_28_36
Theory : sets_1
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