Nuprl Lemma : set-mono
∀A:Type. ∀P:A ⟶ ℙ. (mono(A) ⇒ mono({a:A| P[a]} ))
Proof
Definitions occuring in Statement :
mono: mono(T),
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x]
Lemmas referenced :
subtype-mono,
strong-subtype-set2,
mono_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
sqequalRule,
universeEquality,
independent_isectElimination,
functionEquality,
cumulativity
Latex:
\mforall{}A:Type. \mforall{}P:A {}\mrightarrow{} \mBbbP{}. (mono(A) {}\mRightarrow{} mono(\{a:A| P[a]\} ))
Date html generated:
2016_05_13-PM-04_13_37
Last ObjectModification:
2015_12_26-AM-11_10_28
Theory : subtype_1
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