Nuprl Lemma : subtype-mono
∀[A,B:Type]. (mono(A)) supposing (mono(B) and strong-subtype(A;B))
Proof
Definitions occuring in Statement :
mono: mono(T),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mono: mono(T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
implies: P ⇒ Q,
guard: {T},
label: ...$L... t,
prop: ℙ
Lemmas referenced :
strong-subtype-implies,
is-above_wf,
base_wf,
mono_wf,
strong-subtype_wf,
is-above-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
productElimination,
sqequalRule,
independent_functionElimination,
lemma_by_obid,
isectElimination,
because_Cache,
equalitySymmetry,
lambdaEquality,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A,B:Type]. (mono(A)) supposing (mono(B) and strong-subtype(A;B))
Date html generated:
2016_05_13-PM-04_13_35
Last ObjectModification:
2015_12_26-AM-11_11_12
Theory : subtype_1
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