Nuprl Lemma : fpf-join-domain
∀[A:Type]. ∀f,g:a:A fp-> Top. ∀eq:EqDecider(A). fpf-domain(f ⊕ g) ⊆ fpf-domain(f) @ fpf-domain(g)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
l_contains: A ⊆ B,
append: as @ bs,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_contains: A ⊆ B,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q
Lemmas referenced :
l_all_iff,
fpf-domain_wf,
fpf-join_wf,
top_wf,
l_member_wf,
append_wf,
member_append,
or_wf,
fpf-domain-join,
all_wf,
deq_wf,
fpf_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
hypothesis,
setElimination,
rename,
setEquality,
productElimination,
independent_functionElimination,
because_Cache,
addLevel,
allFunctionality,
impliesFunctionality,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}f,g:a:A fp-> Top. \mforall{}eq:EqDecider(A). fpf-domain(f \moplus{} g) \msubseteq{} fpf-domain(f) @ fpf-domain(g)
Date html generated:
2018_05_21-PM-09_21_38
Last ObjectModification:
2018_02_09-AM-10_18_22
Theory : finite!partial!functions
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