Nuprl Lemma : fpf-disjoint-compatible
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:a:A fp-> B[a]]. f || g supposing l_disjoint(A;fst(f);fst(g))
Proof
Definitions occuring in Statement :
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
l_disjoint: l_disjoint(T;l1;l2),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
l_disjoint: l_disjoint(T;l1;l2),
not: ¬A,
cand: A c∧ B,
false: False
Lemmas referenced :
assert_wf,
deq-member_wf,
l_disjoint_wf,
list_wf,
l_member_wf,
deq_wf,
assert-deq-member
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
productEquality,
lemma_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
setEquality,
applyEquality,
setElimination,
rename,
independent_functionElimination,
independent_pairFormation,
voidElimination
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:a:A fp-> B[a]].
f || g supposing l\_disjoint(A;fst(f);fst(g))
Date html generated:
2018_05_21-PM-09_28_35
Last ObjectModification:
2018_02_09-AM-10_23_49
Theory : finite!partial!functions
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