Nuprl Lemma : fpf-restrict-compatible2
∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:x:A fp-> B[x]].
f || fpf-restrict(g;P) supposing f || g
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
fpf-compatible: f || g,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ
Lemmas referenced :
fpf-compatible-symmetry,
fpf-restrict_wf2,
fpf-restrict-compatible,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
axiomEquality,
productEquality,
cumulativity,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:x:A fp-> B[x]].
f || fpf-restrict(g;P) supposing f || g
Date html generated:
2018_05_21-PM-09_31_34
Last ObjectModification:
2018_02_09-AM-10_25_54
Theory : finite!partial!functions
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