Nuprl Lemma : psub_wf
∀[a,b:formula()]. (a ⊆ b ∈ ℙ)
Proof
Definitions occuring in Statement :
psub: a ⊆ b,
formula: formula(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
psub: a ⊆ b,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
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 :
pimp_wf,
por_wf,
pand_wf,
pnot_wf,
equal_wf,
or_wf,
atom_subtype_base,
formula_wf,
equal-wf-T-base,
formula_ind_wf_simple
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[a,b:formula()]. (a \msubseteq{} b \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-07_13_15
Last ObjectModification:
2016_01_16-AM-09_45_02
Theory : general
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