Nuprl Lemma : combine-pcs_wf
∀[X,Y:polynomial-constraints()]. (combine-pcs(X;Y) ∈ polynomial-constraints())
Proof
Definitions occuring in Statement :
combine-pcs: combine-pcs(X;Y),
polynomial-constraints: polynomial-constraints(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
combine-pcs: combine-pcs(X;Y),
polynomial-constraints: polynomial-constraints(),
subtype_rel: A ⊆r B
Lemmas referenced :
append_wf,
iPolynomial_wf,
list_wf,
polynomial-constraints_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
hypothesisEquality,
independent_pairEquality,
lemma_by_obid,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X,Y:polynomial-constraints()]. (combine-pcs(X;Y) \mmember{} polynomial-constraints())
Date html generated:
2016_05_14-AM-07_08_07
Last ObjectModification:
2015_12_26-PM-01_08_11
Theory : omega
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