Nuprl Lemma : base-CP_wf
base-CP() ∈ ℙ
Proof
Definitions occuring in Statement :
base-CP: base-CP(),
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
base-CP: base-CP(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
bfalse: ff,
nat: ℕ,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
isect2_wf,
nat_wf,
base_wf,
exists_wf,
int_seg_wf,
isect2_subtype_rel,
isect2_subtype_rel2,
bool_wf,
equal_wf,
isect2_decomp,
int_seg_subtype_nat,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
because_Cache,
lambdaEquality,
natural_numberEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
isect_memberEquality,
unionElimination,
equalityElimination,
setElimination,
rename,
productElimination,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
lambdaFormation
Latex:
base-CP() \mmember{} \mBbbP{}
Date html generated:
2017_04_17-AM-09_40_54
Last ObjectModification:
2017_02_27-PM-05_35_52
Theory : fan-theorem
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