Nuprl Lemma : p-inject_wf
∀[A,B:Type]. ∀[f:A ⟶ (B + Top)]. (p-inject(A;B;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
p-inject: p-inject(A;B;f),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
p-inject: p-inject(A;B;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
all_wf,
assert_wf,
can-apply_wf,
equal_wf,
do-apply_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
functionEquality,
functionExtensionality,
applyEquality,
hypothesis,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} (B + Top)]. (p-inject(A;B;f) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-06_32_54
Last ObjectModification:
2017_07_26-PM-04_51_55
Theory : general
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