Nuprl Lemma : fpf-sub_weakening
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> B[a]]. f ⊆ g supposing f = g ∈ a:A fp-> B[a]
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
fpf-sub: f ⊆ g,
all: ∀x:A. B[x],
cand: A c∧ B,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
fpf-sub_wf,
fpf-sub_witness,
equal_wf,
fpf_wf,
deq_wf,
fpf-ap_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
thin,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
functionEquality,
universeEquality,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> B[a]]. f \msubseteq{} g supposing f = g
Date html generated:
2018_05_21-PM-09_19_09
Last ObjectModification:
2018_02_09-AM-10_17_26
Theory : finite!partial!functions
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