Nuprl Lemma : pnegate_wf
∀[x:formula()]. (pnegate(x) ∈ formula())
Proof
Definitions occuring in Statement :
pnegate: pnegate(x),
formula: formula(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pnegate: pnegate(x),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
formula_ind_wf_simple,
formula_wf,
pnot_wf,
pvar_wf,
por_wf,
pand_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
atomEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:formula()]. (pnegate(x) \mmember{} formula())
Date html generated:
2016_05_15-PM-07_18_39
Last ObjectModification:
2015_12_27-AM-11_28_11
Theory : general
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