Nuprl Lemma : decidable__set_leq
∀p:PosetSig. ∀a,b:|p|. Dec(a ≤ b)
Proof
Definitions occuring in Statement :
set_leq: a ≤ b,
set_car: |p|,
poset_sig: PosetSig,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
set_leq: a ≤ b,
all: ∀x:A. B[x],
member: t ∈ T,
infix_ap: x f y,
uall: ∀[x:A]. B[x]
Lemmas referenced :
decidable__assert,
set_le_wf,
set_car_wf,
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
applyEquality,
isectElimination,
hypothesisEquality,
hypothesis
Latex:
\mforall{}p:PosetSig. \mforall{}a,b:|p|. Dec(a \mleq{} b)
Date html generated:
2016_05_15-PM-00_04_11
Last ObjectModification:
2015_12_26-PM-11_28_37
Theory : sets_1
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