Nuprl Lemma : union-mono
∀A,B:Type. ((mono(A) ∧ mono(B)) ⇒ mono(A + B))
Proof
Definitions occuring in Statement :
mono: mono(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
mono: mono(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
prop: ℙ,
guard: {T}
Lemmas referenced :
is-above-inl,
is-above-inr,
is-above_wf,
base_wf,
and_wf,
mono_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
unionElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
sqequalRule,
inlEquality,
because_Cache,
inrEquality,
unionEquality,
universeEquality
Latex:
\mforall{}A,B:Type. ((mono(A) \mwedge{} mono(B)) {}\mRightarrow{} mono(A + B))
Date html generated:
2016_05_13-PM-04_13_54
Last ObjectModification:
2015_12_26-AM-11_10_03
Theory : subtype_1
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