Nuprl Lemma : fpf-join-compatible-left
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B,C,D,E,F,G:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[g:a:A fp-> C[a]]. ∀[h:a:A fp-> D[a]].
({(f ⊕ g || h) supposing (g || h and f || h)}) supposing
((∀a:A. (E[a] ⊆r G[a])) and
(∀a:A. (F[a] ⊆r G[a])) and
(∀a:A. (D[a] ⊆r F[a])) and
(∀a:A. (D[a] ⊆r E[a])) and
(∀a:A. (C[a] ⊆r F[a])) and
(∀a:A. (B[a] ⊆r E[a])))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-join-dom2,
assert_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
subtype-fpf2,
subtype_top,
fpf-compatible_wf,
all_wf,
subtype_rel_wf,
fpf_wf,
deq_wf,
bool_wf,
equal_functionality_wrt_subtype_rel2,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B,C,D,E,F,G:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[g:a:A fp-> C[a]].
\mforall{}[h:a:A fp-> D[a]].
(\{(f \moplus{} g || h) supposing (g || h and f || h)\}) supposing
((\mforall{}a:A. (E[a] \msubseteq{}r G[a])) and
(\mforall{}a:A. (F[a] \msubseteq{}r G[a])) and
(\mforall{}a:A. (D[a] \msubseteq{}r F[a])) and
(\mforall{}a:A. (D[a] \msubseteq{}r E[a])) and
(\mforall{}a:A. (C[a] \msubseteq{}r F[a])) and
(\mforall{}a:A. (B[a] \msubseteq{}r E[a])))
Date html generated:
2015_07_17-AM-11_11_57
Last ObjectModification:
2015_01_28-AM-07_46_08
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