Nuprl Lemma : fpf-compatible-update2
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:a:A fp-> B[a]]. f || f ⊕ g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-compatible: f || g,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
fpf-ap_wf,
fpf-join-ap-left,
iff_weakening_equal,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
fpf-join_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
applyEquality,
lambdaEquality,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
functionExtensionality,
cumulativity,
sqequalRule,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
productEquality,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
isect_memberFormation,
dependent_functionElimination,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:a:A fp-> B[a]]. f || f \moplus{} g
Date html generated:
2018_05_21-PM-09_28_42
Last ObjectModification:
2018_02_09-AM-10_23_53
Theory : finite!partial!functions
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