Nuprl Lemma : finite-type-union
∀[A,B:Type]. (finite-type(A) ⇒ finite-type(B) ⇒ finite-type(A + B))
Proof
Definitions occuring in Statement :
finite-type: finite-type(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
finite-type-iff-list,
append_wf,
map_wf,
member_append,
member_map,
l_member_wf,
or_wf,
exists_wf,
and_wf,
equal_wf,
all_wf,
finite-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
unionEquality,
dependent_pairFormation,
lambdaEquality,
inlEquality,
inrEquality,
because_Cache,
dependent_functionElimination,
addLevel,
orFunctionality,
sqequalRule,
universeEquality,
unionElimination,
inlFormation,
independent_pairFormation,
inrFormation
Latex:
\mforall{}[A,B:Type]. (finite-type(A) {}\mRightarrow{} finite-type(B) {}\mRightarrow{} finite-type(A + B))
Date html generated:
2016_05_15-PM-04_26_24
Last ObjectModification:
2015_12_27-PM-02_51_16
Theory : general
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