Nuprl Lemma : fpf-compatible_monotonic-guard
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f1,g1,f2,g2:a:A fp-> B[a]].
({f1 || g1 supposing f2 || g2}) supposing (g1 ⊆ g2 and f1 ⊆ f2)
Proof
Definitions occuring in Statement :
fpf-compatible: f || g,
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T}
Lemmas referenced :
fpf-compatible_monotonic
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f1,g1,f2,g2:a:A fp-> B[a]].
(\{f1 || g1 supposing f2 || g2\}) supposing (g1 \msubseteq{} g2 and f1 \msubseteq{} f2)
Date html generated:
2018_05_21-PM-09_20_01
Last ObjectModification:
2018_02_09-AM-10_17_49
Theory : finite!partial!functions
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