Nuprl Lemma : subtype-Sierpinski
(ℕ ⟶ 𝔹) ⊆r Sierpinski
Proof
Definitions occuring in Statement :
Sierpinski: Sierpinski,
nat: ℕ,
bool: 𝔹,
subtype_rel: A ⊆r B,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
Sierpinski: Sierpinski,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
subtype_quotient,
nat_wf,
bool_wf,
iff_wf,
equal_wf,
Sierpinski-bottom_wf,
two-class-equiv-rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
independent_isectElimination
Latex:
(\mBbbN{} {}\mrightarrow{} \mBbbB{}) \msubseteq{}r Sierpinski
Date html generated:
2019_10_31-AM-06_35_27
Last ObjectModification:
2015_12_28-AM-11_21_31
Theory : synthetic!topology
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