Nuprl Lemma : fpf-compatible-mod_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> B[a]]. ∀[R:⋂a:A. (B[a] ⟶ B[a] ⟶ 𝔹)].
(fpf-compatible-mod(A;a.B[a];eq;
R;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
fpf-compatible-mod: fpf-compatible-mod,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-compatible-mod: fpf-compatible-mod,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
all_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
not_wf,
fpf-ap_wf,
equal_wf,
bool_wf,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionEquality,
productEquality,
because_Cache,
applyEquality,
functionExtensionality,
hypothesis,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
axiomEquality,
isectEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> B[a]]. \mforall{}[R:\mcap{}a:A. (B[a] {}\mrightarrow{} B[a] {}\mrightarrow{} \mBbbB{})].
(fpf-compatible-mod(A;a.B[a];eq;
R;f;g) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-09_20_05
Last ObjectModification:
2018_02_09-AM-10_17_51
Theory : finite!partial!functions
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