Nuprl Lemma : strong-subtype_transitivity
∀[A,B,C:Type]. (strong-subtype(A;C)) supposing (strong-subtype(B;C) and strong-subtype(A;B))
Proof
Definitions occuring in Statement :
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,
implies: P ⇒ Q,
guard: {T},
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
strong-subtype-implies,
subtype_rel_transitivity,
exists_wf,
equal_wf,
strong-subtype_witness,
strong-subtype_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
productElimination,
independent_isectElimination,
independent_pairFormation,
lambdaEquality,
setEquality,
sqequalRule,
applyEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
setElimination,
rename,
dependent_functionElimination
Latex:
\mforall{}[A,B,C:Type]. (strong-subtype(A;C)) supposing (strong-subtype(B;C) and strong-subtype(A;B))
Date html generated:
2019_06_20-PM-00_27_52
Last ObjectModification:
2018_09_12-PM-11_28_24
Theory : subtype_1
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